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-The classical SIR model assumes that a population can be divided into three distinct compartments (see e.g. Bloomfiled[2009, pp 149]): S is the proportion of susceptibles, I is the proportion of infected persons and R is the proportion of persons that have recovered from infection and are now immune against the disease. This model was originally developed in 1927 by Kermack and McKendrik.
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LSUrQU5OT1RBVElPTkc2Jy0lKUJPVU5EU19YRzYjJCIjNSEiIi0lKUJPVU5EU19ZRzYjJCIiIUYqLSUtQk9VTkRTX1dJRFRIRzYjJCIlXURGKi0lLkJPVU5EU19IRUlHSFRHNiMkIiRxJkYqLSUpQ0hJTERSRU5HNiI=
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- Figure 1
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-The classic SIR model can be described by three functions:
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-The basic reproduction ratio LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGNC8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRi82I1EhRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y6RjVGNw==, for the classic SIR model as defined above, can be derived as:
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-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-LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGNC8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRi82I1EhRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIn5GJ0Y1RjcvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZURjVGNw== is the number of secondary infections that is produced by one primary infection in a wholly susceptible population. Only when LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGNC8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRi82I1EhRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIn5GJ0Y1RjcvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZURjVGNw== > 1, does an epidemic occurs. 1/\316\263 is the average infectious period. Setting equations (1)-(3) equal to zero and solving these for the equilibrium solutions of 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 and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtRiw2JlEidEYnRi9GMkY1RjIvRjZRJ25vcm1hbEYnRjJGQC1GLDYjUSFGJ0YyRkA= yields an equilibrium whenever LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRInRGJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGQC1JI21vR0YkNi1RIj1GJ0ZALyUmZmVuY2VHRj8vJSpzZXBhcmF0b3JHRj8vJSlzdHJldGNoeUdGPy8lKnN5bW1ldHJpY0dGPy8lKGxhcmdlb3BHRj8vJS5tb3ZhYmxlbGltaXRzR0Y/LyUnYWNjZW50R0Y/LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGVi1JI21uR0YkNiRRIzAuRidGQEY9RkA=
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-Notes: (1) The basic reproduction ratio LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GLzYjUSFGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEifkYnRjUvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZSLyUrZXhlY3V0YWJsZUdGNEY1is often ambiguously denoted LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYsNiZRIjBGJ0YvRjJGNS8lL3N1YnNjcmlwdHNoaWZ0R0Y6, leading to potential confusion with LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiQtSSNtbkdGJDYlUSIwRidGMi9GNlEnbm9ybWFsRidGQUYyRkFGQQ==, which is the initial value of the recovered function LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiQtRiw2JlEidEYnRi9GMkY1L0Y2USdub3JtYWxGJ0YyRkBGQA==. (2) Not all combinations of infection and removal rates within the ranges of the interactive model below will match a real existing infectious disease. (3)The SIR model exists in different flavors and parametrizations, the model as presented here follows Bloomfield[2009].
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-<Text-field style="Heading 2" layout="Heading 2"><Font family="Arial">Interactive SIR model: Infectious Disease Nonlinear Compartment Model 1</Font></Text-field>
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-LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
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-<Text-field style="Heading 2" family="Arial" layout="Heading 2"><Font family="Arial">Background</Font></Text-field>
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-The classical SIR model assumes that a population can be divided into three distinct compartments (see e.g. Bloomfield[2009, pp 149]): S is the proportion of susceptibles, I is the proportion of infected persons and R is the proportion of persons that have recovered from infection and are now immune against the disease. This model was originally developed in 1927 by Kermack and McKendrik.
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-One extension to the classic SIR model is to add births and deaths to the model. Thus there is an inflow of new susceptibles and an outflow from all three compartments. In its simplest form, the birth rate is set equal to the death rate which is assumed not to be related to the infectious disease.
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LSUrQU5OT1RBVElPTkc2Jy0lKUJPVU5EU19YRzYjJCIjNSEiIi0lKUJPVU5EU19ZRzYjJCIiIUYqLSUtQk9VTkRTX1dJRFRIRzYjJCIlIXAjRiotJS5CT1VORFNfSEVJR0hURzYjJCIkISoqRiotJSlDSElMRFJFTkc2Ig==
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- Figure 1
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-The extended SIR model with births and deaths can be described by three functions:
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-The basic reproduction ratio LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGNC8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRi82I1EhRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y6RjVGNw==, for the SIR model as defined above, can be derived as:
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-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-LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGNC8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRi82I1EhRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIn5GJ0Y1RjcvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZURjVGNw== is the number of secondary infections that is produced by one primary infection in a wholly susceptible population. Only when LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGNC8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRi82I1EhRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIn5GJ0Y1RjcvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZURjVGNw== > 1, does an epidemic occurs. 1/(\316\263+\316\274) is the average infectious period. Setting equations (1)-(3) equal to zero and solving these for the equilibrium solutions of 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 and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtRiw2JlEidEYnRi9GMkY1RjIvRjZRJ25vcm1hbEYnRjJGQC1GLDYjUSFGJ0YyRkA= in dependence of the parameters LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JlEnJiM5NTY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYuUSIsRidGMkY0LyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRjg2LlEifkYnRjJGNEY7L0Y+RjFGQEZCRkRGRkZIRkovRk5GTC1GLDYmUScmIzk0NjtGJ0YvRjJGNEY3RjJGNA==and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEnJiM5NDc7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYuUSJ+RidGMkY0LyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGS0Y3RjJGNA==(e.g. by using the Maple procedure solve()) provides the following equilibrium solution:
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-Notes: (1) The basic reproduction ratio LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GLzYjUSFGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEifkYnRjUvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZSLyUrZXhlY3V0YWJsZUdGNEY1is often ambiguously denoted LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYsNiZRIjBGJ0YvRjJGNS8lL3N1YnNjcmlwdHNoaWZ0R0Y6, leading to potential confusion with LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiQtSSNtbkdGJDYlUSIwRidGMi9GNlEnbm9ybWFsRidGQUYyRkFGQQ==, which is the initial value of the recovered function LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiQtRiw2JlEidEYnRi9GMkY1L0Y2USdub3JtYWxGJ0YyRkBGQA==. (2) Not all combinations of infection and removal rates within the ranges of the interactive model below will match a real existing infectious disease. (3)The SIR model exists in different flavors and parametrizations, the model as presented here follows Bloomfield[2009].
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-<Text-field style="Heading 2" layout="Heading 2"><Font family="Arial">Interactive Extended SIR model: Infectious Disease Nonlinear Compartment Model 2</Font></Text-field>
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-LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
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-The SEIR model is an extension of the classical SIR (Susceptibles, Infected, Recovered) model which was originally developed by Kermack/McKendrick[1927]: a fourth compartment is added which contains exposed persons which are infected but are not yet infectious. The SEIR (Susceptibles, Exposed, Infectious, Recovered) model as presented here covers also births and deaths. Persons in all compartments are measured as fractions of the total population. The birth rate is set equal to the death rate which is assumed not to be related to the infectious disease. It can be shown that the inverse of the death rate is equal to the life expectancy.
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LSUrQU5OT1RBVElPTkc2Jy0lKUJPVU5EU19YRzYjJCIjNSEiIi0lKUJPVU5EU19ZRzYjJCIiIUYqLSUtQk9VTkRTX1dJRFRIRzYjJCIlK01GKi0lLkJPVU5EU19IRUlHSFRHNiMkIiQhKipGKi0lKUNISUxEUkVORzYi
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- Figure 1
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-The extended SEIR model with births and deaths can be described by four functions:
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-The basic reproduction ratio LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEnJiM5NjE7RicvJSdmYW1pbHlHUSZBcmlhbEYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRi82I1EhRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y7RjIvJStleGVjdXRhYmxlR0Y3Rjg=, for the SIR model as defined above, can be derived as:
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-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-LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GLzYjUSFGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEifkYnRjUvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZSLyUrZXhlY3V0YWJsZUdGNEY1 is the number of secondary infections that is produced by one primary infection in a wholly susceptible population. Only when LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GLzYjUSFGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEifkYnRjUvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZSLyUrZXhlY3V0YWJsZUdGNEY1 > 1, does an epidemic occurs. 1/(\316\263+\316\274) is the average infectious period. Setting equations (1)-(4) equal to zero and solving these for the equilibrium solutions of 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, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiRUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiQtRiw2JlEidEYnRi9GMkY1L0Y2USdub3JtYWxGJ0YyRkBGQA== and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRInRGJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGQC1GLDYjUSFGJ0Y9RkA= in dependence of the parameters 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 and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEnJiM5NDc7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIn5GJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGSUY1LyUrZXhlY3V0YWJsZUdGMUYy(e.g. by using the Maple procedure solve()) provides the following equilibrium solution:JSFH
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-Notes: (1) The basic reproduction ratio LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GLzYjUSFGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEifkYnRjUvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZSLyUrZXhlY3V0YWJsZUdGNEY1is often ambiguously denoted LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYsNiZRIjBGJ0YvRjJGNS8lL3N1YnNjcmlwdHNoaWZ0R0Y6, leading to potential confusion with LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiQtSSNtbkdGJDYlUSIwRidGMi9GNlEnbm9ybWFsRidGQUYyRkFGQQ==, which is the initial value of the recovered function LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiQtRiw2JlEidEYnRi9GMkY1L0Y2USdub3JtYWxGJ0YyRkBGQA==. (2) Not all combinations of infection and removal rates within the ranges of the interactive model below will match a real existing infectious disease. (3) The SEIR model exists in different flavors and parametrizations, the model as presented here follows Keeling/Rohani[2008].
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-<Text-field style="Heading 2" layout="Heading 2"><Font family="Arial">Interactive SEIR model: Infectious Disease Nonlinear Compartment Model 3</Font></Text-field>
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-Example 1. Real Distinct Eigenvalues
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-Enter the three rows of the matrix A and the initialization vector.
-Click anywhere into the math area below and press [Enter].
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-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-Example 1. Real Distinct Eigenvalues (continued)
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-Using the P matrix you computed by hand.
-Enter the three rows of the matrix A, the initialization vector, and the three rows of your P matrix.
-Click anywhere into the math area below and press [Enter].
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-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-LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
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-JSFH
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-Example 2. Real Distinct Eigenvalues
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-Enter the three rows of the matrix A and the initialization vector.
-Click anywhere into the math area below and press [Enter].
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-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-JSFH
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-Example 2. Real Distinct Eigenvalues (continued)
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-Using the P matrix you computed by hand.
-Enter the three rows of the matrix A, the initialization vector, and the three rows of your P matrix.
-Click anywhere into the math area below and press [Enter].
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-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-LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
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-JSFH
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-Example 3. Real Distinct Eigenvalues
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-
-Enter the three rows of the matrix A and the initialization vector.
-Click anywhere into the math area below and press [Enter].
-
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-
-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-LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
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-
-Example 3. Real Distinct Eigenvalues (continued)
-
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-Using the P matrix you computed by hand.
-Enter the three rows of the matrix A, the initialization vector, and the three rows of your P matrix.
-Click anywhere into the math area below and press [Enter].
-
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-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-JSFH
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-Example 4. Complex Eigenvalues
-
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-
-Enter the three rows of the matrix A and the initialization vector.
-Click anywhere into the math area below and press [Enter].
-
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-
-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-JSFH
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-Example 4. Complex Eigenvalues (continued)
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-Using the P matrix you computed by hand.
-Enter the three rows of the matrix A, the initialization vector, and the three rows of your P matrix.
-Click anywhere into the math area below and press [Enter].
-
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-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-JSFH
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-Example 5. Complex Eigenvalues
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-Enter the three rows of the matrix A and the initialization vector.
-Click anywhere into the math area below and press [Enter].
-
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-LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUkjbWlHRiQ2JlEoJmFscGhhO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lMGZvbnRfc3R5bGVfbmFtZUdRKTJEfklucHV0RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LlEqJmNvbG9uZXE7RidGMkY1LyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYmUS5mbG93Q3VydmVQbHVzRicvRjBRJXRydWVGJ0YyL0Y2USdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JS1GIzYrLUZXNictRiM2KC1JI21uR0YkNiVRIjBGJ0YyRjUtRjk2LlEiLEYnRjJGNUY8L0Y/RlNGQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZOUSwwLjMzMzMzMzNlbUYnLUZqbjYlUSIyRidGMkY1Rl1vRmluRjVGMkY1LyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRl1vLUZXNictRiM2KS1GOTYuUSomdW1pbnVzMDtGJ0YyRjVGPEY+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZmcEZlb0Zdb0ZpbkZdb0ZpbkY1RjJGNUZob0ZbcEZdby1GVzYnLUYjNihGZW9GXW9GaW5GXW8tRmpuNiVRIjZGJ0YyRjVGNUYyRjVGaG9GW3BGXW8tRlc2Jy1GIzYoLUZqbjYlUSI0RidGMkY1Rl1vLUZqbjYlUSI4RidGMkY1Rl1vLUZqbjYlUSMxMkYnRjJGNUY1RjJGNUZob0ZbcC1GLDYjUSFGJ0Y1RjJGNS1GOTYuUSI6RidGMkY1RjxGPkZARkJGREZGRkhGSkZNLUY5Ni5RIn5GJ0YyRjVGPEY+RkBGQkZERkZGSEZhby9GTkZib0Zici8lK2V4ZWN1dGFibGVHRjFGNQ==
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-Example 5. Complex Eigenvalues (continued)
-
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-Using the P matrix you computed by hand.
-Enter the three rows of the matrix A, the initialization vector, and the three rows of your P matrix.
-Click anywhere into the math area below and press [Enter].
-
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-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-JSFH
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-Example 6. Complex Eigenvalues
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-Enter the three rows of the matrix A and the initialization vector.
-Click anywhere into the math area below and press [Enter].
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-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-JSFH
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-Example 6. Complex Eigenvalues (continued)
-
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-
-Using the P matrix you computed by hand.
-Enter the three rows of the matrix A, the initialization vector, and the three rows of your P matrix.
-Click anywhere into the math area below and press [Enter].
-
-
-
-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-JSFH
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-Example 7. Real Repeated Eigenvalues
-
-
-
-Enter the three rows of the matrix A and the initialization vector.
-Click anywhere into the math area below and press [Enter].
-
-
-
-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-LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
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-JSFH
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-Example 7. Real Repeated Eigenvalues (continued)
-
-
-
-Using the P matrix you computed by hand.
-Enter the three rows of the matrix A, the initialization vector, and the three rows of your P matrix.
-Click anywhere into the math area below and press [Enter].
-
-
-
-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-JSFH
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-Example 8. Real Repeated Eigenvalues
-
-
-
-Enter the three rows of the matrix A and the initialization vector.
-Click anywhere into the math area below and press [Enter].
-
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-
-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-Example 8. Real Repeated Eigenvalues (continued)
-
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-Using the P matrix you computed by hand.
-Enter the three rows of the matrix A, the initialization vector, and the three rows of your P matrix.
-Click anywhere into the math area below and press [Enter].
-
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-LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JlEoJmFscGhhO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lMGZvbnRfc3R5bGVfbmFtZUdRKTJEfklucHV0RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LlEqJmNvbG9uZXE7RidGMkY1LyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYmUTBmbG93Q3VydmVJbnB1dFBGJy9GMFEldHJ1ZUYnRjIvRjZRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNi4tRiw2I1EhRictRiM2J0Zlbi1GIzYpLUZXNictRiM2Ki1JI21uR0YkNiVRIjNGJ0YyRjUtRjk2LlEiLEYnRjJGNUY8L0Y/RlNGQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZOUSwwLjMzMzMzMzNlbUYnLUY5Ni5RKiZ1bWludXMwO0YnRjJGNUY8Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZORmBwLUZhbzYlUSIxRidGMkY1RmRvLUZhbzYlUSIyRidGMkY1RjJGNUYyRjUvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGZG8tRlc2Jy1GIzYqRmBvRmRvRlxwRmJwRmRvLUZhbzYlUSI2RidGMkY1RjJGNUYyRjVGaHBGW3FGZG8tRlc2Jy1GIzYrRlxwRmVwRmRvRmVwRmRvRlxwRmVwRjJGNUYyRjVGaHBGW3FGMkY1RmVuRjJGNUZlbkZkby1GVzYnLUYjNigtRmFvNiVRIjRGJ0YyRjVGZG8tRmFvNiVRIjhGJ0YyRjVGZG8tRmFvNiVRIzEyRidGMkY1RjVGMkY1RmhwRltxRmRvLUZXNictRiM2KkZccC1JJm1mcmFjR0YkNihGYnAtRiM2JEZlcEY1LyUubGluZXRoaWNrbmVzc0dGZHAvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGY3MvJSliZXZlbGxlZEdGMUZkb0ZicEZkb0ZccEZlcEY1RjJGNUZocEZbcUZkby1GVzYnLUYjNilGXHAtRltzNihGYG8tRiM2JkZlcEZSRjJGVEZfc0Zhc0Zkc0Zmc0Zkb0ZicEZkby1GYW82JVEiMEYnRjJGNUY1RjJGNUZocEZbcUZkby1GVzYnLUYjNihGYnBGZG9GYHRGZG9GYnBGNUYyRjVGaHBGW3FGNUYyRjUtRjk2LVEiOkYnRjVGPEY+RkBGQkZERkZGSEZKRk0vJStleGVjdXRhYmxlR0YxRjU=
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-JSFH
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-Example 9. Real Repeated Eigenvalues
-
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-
-Hirsch and Smale Example 2, p. 112. Check new flowCurvePlus with one Eigenvalue with multiplicity 2 but S + N needed
-since only one basis eigenvector, thus must find the kernel of Caley-Hamilton power operator for the basis.
-Click anywhere into the math area below and press [Enter].
-
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-
-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-Example 9. Real Repeated Eigenvalues (continued)
-
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-Using the P matrix you computed by hand.
-Enter the three rows of the matrix A, the initialization vector, and the three rows of your P matrix.
-Click anywhere into the math area below and press [Enter].
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-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-Example 10. Real Repeated Eigenvalues
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-Enter the three rows of the matrix A and the initialization vector.
-Click anywhere into the math area below and press [Enter].
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-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-LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
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-Example 10. Real Repeated Eigenvalues (continued)
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-Using the P matrix you computed by hand.
-Enter the three rows of the matrix A, the initialization vector, and the three rows of your P matrix.
-Click anywhere into the math area below and press [Enter].
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-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-Linear Compartment Model: Recall our previous Brine Tank (used in water softeners) Cascade Problem for an Open System
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LSUrQU5OT1RBVElPTkc2Jy0lKUJPVU5EU19YRzYjJCIiISEiIi0lKUJPVU5EU19ZR0YnLSUtQk9VTkRTX1dJRFRIRzYjJCIlIVEpRiotJS5CT1VORFNfSEVJR0hURzYjJCIlcUtGKi0lKUNISUxEUkVORzYi
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-Brine Tank Cascade Problem 1. Real Distinct Eigenvalues
-Enter the three rows of the matrix A and the initialization vector.
-Click anywhere into the math area below and press [Enter].
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-LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
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-Brine Tank Cascade Problem 1. Real Distinct Eigenvalues (continued)
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-Using the P matrix you computed by hand.
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-Enter the three rows of the matrix A, the initialization vector, and the three rows of your P matrix.
-Click anywhere into the math area below and press [Enter].
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-LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JlEoJmFscGhhO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lMGZvbnRfc3R5bGVfbmFtZUdRKTJEfklucHV0RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LlEqJmNvbG9uZXE7RidGMkY1LyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYmUTBmbG93Q3VydmVJbnB1dFBGJy9GMFEldHJ1ZUYnRjIvRjZRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNi0tRlc2Jy1GIzYpLUY5Ni5RKiZ1bWludXMwO0YnRjJGNUY8Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZORl1vLUkmbWZyYWNHRiQ2KC1JI21uR0YkNiVRIjFGJ0YyRjUtRiM2JC1GY282JVEiMkYnRjJGNUY1LyUubGluZXRoaWNrbmVzc0dGZW8vJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGX3AvJSliZXZlbGxlZEdGMS1GOTYuUSIsRidGMkY1RjwvRj9GU0ZARkJGREZGRkgvRktRJjAuMGVtRicvRk5RLDAuMzMzMzMzM2VtRictRmNvNiVRIjBGJ0YyRjVGZHBGXHFGNUYyRjUvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGZHAtRlc2Jy1GIzYpRl9vRmRwRmluLUZgbzYoRmJvLUYjNiQtRmNvNiVRIjRGJ0YyRjVGNUZbcEZdcEZgcEZicEZkcEZccUY1RjJGNUZfcUZicUZkcC1GVzYnLUYjNilGXHFGZHBGaXFGZHBGaW4tRmBvNihGYm8tRiM2JC1GY282JVEiNkYnRjJGNUY1RltwRl1wRmBwRmJwRjVGMkY1Rl9xRmJxRmRwLUZXNictRiM2KEZdckZkcC1GY282JVEiOEYnRjJGNUZkcC1GY282JVEjMTJGJ0YyRjVGNUYyRjVGX3FGYnFGZHAtRiM2KC1GVzYnLUYjNihGXHFGZHAtRmBvNihGaG8tRiM2Ji1GY282JVEiM0YnRjJGNUZSRjJGVEZbcEZdcEZgcEZicEZkcEZccUY1RjJGNUZfcUZicUZkcC1GVzYnLUYjNipGaW4tRmBvNihGYm9GXXRGW3BGXXBGYHBGYnBGZHBGaW4tRmBvNihGXXJGXXRGW3BGXXBGYHBGYnBGZHBGXHFGNUYyRjVGX3FGYnFGZHAtRlc2Jy1GIzYoRmJvRmRwRmJvRmRwRmJvRjVGMkY1Rl9xRmJxRjUtRiw2I1EhRidGNUYyRjUtRjk2LVEiOkYnRjVGPEY+RkBGQkZERkZGSEZKRk0vJStleGVjdXRhYmxlR0YxRjU=
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-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-LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
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-JSFH
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-Linear Compartment Model: Brine Tank Cascade Problem for a Closed System
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LSUrQU5OT1RBVElPTkc2Jy0lKUJPVU5EU19YRzYjJCIiISEiIi0lKUJPVU5EU19ZR0YnLSUtQk9VTkRTX1dJRFRIRzYjJCIlIVEpRiotJS5CT1VORFNfSEVJR0hURzYjJCIlP0tGKi0lKUNISUxEUkVORzYi
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-Brine Tank Cascade Problem 2. Complex Eigenvalues
-Enter the three rows of the matrix A and the initialization vector.
-Click anywhere into the math area below and press [Enter].
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-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-JSFHJSFH
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-Brine Tank Cascade Problem 2. Complex Eigenvalues (continued)
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-Using the P matrix you computed by hand.
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-Enter the three rows of the matrix A, the initialization vector, and the three rows of your P matrix.
-Click anywhere into the math area below and press [Enter].
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-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-JSFH
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-Brine Tank Cascade Problem 3. Complex Eigenvalues
-Enter the three rows of the matrix A and the initialization vector.
-Click anywhere into the math area below and press [Enter].
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-LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
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-LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
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-Brine Tank Cascade Problem 3. Complex Eigenvalues (continued)
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-Using the P matrix you computed by hand.
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-Enter the three rows of the matrix A, the initialization vector, and the three rows of your P matrix.
-Click anywhere into the math area below and press [Enter].
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-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-<Text-field style="Heading 1" layout="Heading 1">3x3 Eigenvalue & Eigenvector Examples: Flow Curves for Drug Absorption Model Dynamical Systems</Text-field>
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LSUrQU5OT1RBVElPTkc2Jy0lKUJPVU5EU19YRzYjJCIjNSEiIi0lKUJPVU5EU19ZRzYjJCIiIUYqLSUtQk9VTkRTX1dJRFRIRzYjJCIlIUgoRiotJS5CT1VORFNfSEVJR0hURzYjJCIlNVFGKi0lKUNISUxEUkVORzYi
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-Click on the edge of the image below to see vcr controls (in the task bar above) to run the animation.
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-Drug Absorption Model Linear Solution Functions: General Percent Concentration Functions
-Click anywhere into the math area below and press [Enter].
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-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-Drug Absorption Model Linear Solution Functions: Specific Percent Concentration Functions for start values of the animation above.
-Click anywhere into the math area below and press [Enter].
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-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-Note that these Linear Solution Functions above can be found by soving the eigenvalue problem immediately below:
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-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-Absorption Model Problem 1. Real Distinct Eigenvalues
-Enter the three rows of the matrix A and the initialization vector.
-Click anywhere into the math area below and press [Enter].
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-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-<Text-field style="Heading 1" layout="Heading 1">Drug Absorption Model</Text-field><Text-field style="Normal" layout="Normal">Define general model for first-order absorption with metabolite concentration, which specializes</Text-field><Text-field style="Normal" layout="Normal">to the first-order absorption model with metabolite elimination when k4 = 0, and to the standard
-first-order absorption model when k3 = k4 = 0.</Text-field>
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-<Text-field style="Heading 1" layout="Heading 1">Flow Curve Plus Code</Text-field>
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2MFEkZW5kRidGXnBGMkZgcEZicEZGRklGS0ZNRk9GUUZTRmRwRmVwRkJGWkZfekZcckZfXGxGQA==
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-<Text-field style="Heading 1" layout="Heading 1">Flow Curve Code</Text-field>
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-LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzZiXWwtSSNtaUdGJDYmUSV3aXRoRicvJSdpdGFsaWNHUSV0cnVlRicvJTBmb250X3N0eWxlX25hbWVHUSkyRH5JbnB1dEYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JS1GIzYlLUYsNiZRLkxpbmVhckFsZ2VicmFGJ0YvRjJGNUYyL0Y2USdub3JtYWxGJ0YyRkAtSSNtb0dGJDYuUSI6RidGMkZALyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZILyUpc3RyZXRjaHlHRkgvJSpzeW1tZXRyaWNHRkgvJShsYXJnZW9wR0ZILyUubW92YWJsZWxpbWl0c0dGSC8lJ2FjY2VudEdGSC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlctSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdRJjAuMGVtRicvJSZkZXB0aEdGaW4vJSpsaW5lYnJlYWtHUShuZXdsaW5lRictRiw2J1EqZmxvd0N1cnZlRidGLy8lK2ZvcmVncm91bmRHUSpbMCwwLDI1NV1GJ0YyRjUtRkM2LlEqJmNvbG9uZXE7RidGMkZARkZGSUZLRk1GT0ZRRlNGVUZYLUZDNjBRJXByb2NGJy8lJWJvbGRHRjFGMi9GNlElYm9sZEYnLyUrZm9udHdlaWdodEdGYXBGRkZJRktGTUZPRlFGUy9GVkZcby9GWUZcby1GOTYlLUYjNjEtRiw2JlErcm93MVZlY3RvckYnRi9GMkY1LUZDNi5RIixGJ0YyRkBGRi9GSkYxRktGTUZPRlFGU0ZkcC9GWVEsMC4zMzMzMzMzZW1GJy1GLDYmUStyb3cyVmVjdG9yRidGL0YyRjVGXXEtRiw2JlErcm93M1ZlY3RvckYnRi9GMkY1Rl1xLUYsNiZRK2luaXRWZWN0b3JGJ0YvRjJGNUZdcS1GLDYmUSplaWdlblNvcnRGJ0YvRjJGNS1GQzYuUS0mUHJvcG9ydGlvbjtGJ0YyRkBGRkZJRktGTUZPRlFGU0ZVRlgtRiw2JlEoaW50ZWdlckYnRi9GMkY1RmhvLUkjbW5HRiQ2JVEiMEYnRjJGQEYyRkBGMkZALUYsNiNRIUYnRlotRkM2MFEmbG9jYWxGJ0ZecEYyRmBwRmJwRkZGSUZLRk1GT0ZRRlNGZHBGZXAtRkM2LlEifkYnRjJGQEZGRklGS0ZNRk9GUUZTRmRwRmVwLUYsNiZRIkFGJ0YvRjJGNUZdcS1GLDYmUSZpbml0VkYnRi9GMkY1Rl1xLUYsNiZRIktGJ0YvRjJGNUZdcS1GLDYmUSdldmVjc0FGJ0YvRjJGNUZdcS1GLDYmUShldmVjc0ExRidGL0YyRjVGXXEtRiw2JlErZXZlY3NBMVZhbEYnRi9GMkY1Rl1xLUYsNiZRK2V2ZWNzQTFNdWxGJ0YvRjJGNUZdcS1GLDYmUStldmVjc0ExVmVjRidGL0YyRjVGXXEtRiw2JlEoZXZlY3NBMkYnRi9GMkY1Rl1xLUYsNiZRK2V2ZWNzQTJWYWxGJ0YvRjJGNUZdcS1GLDYmUStldmVjc0EyTXVsRidGL0YyRjVGXXEtRiw2JlErZXZlY3NBMlZlY0YnRi9GMkY1Rl1xRlpGX3MtRiw2JlEoZXZlY3NBM0YnRi9GMkY1Rl1xLUYsNiZRK2V2ZWNzQTNWYWxGJ0YvRjJGNUZdcS1GLDYmUStldmVjc0EzTXVsRidGL0YyRjVGXXEtRiw2JlErZXZlY3NBM1ZlY0YnRi9GMkY1Rl1xLUYsNiZRIlBGJ0YvRjJGNUZdcS1GLDYmUSVpbnZQRidGL0YyRjVGXXEtRiw2JlEiTEYnRi9GMkY1Rl1xLUYsNiZRKCZhbHBoYTtGJy9GMEZIRjJGQEZCRlpGYnNGaG8tRiw2JlEnTWF0cml4RidGL0YyRjUtRjk2JS1GIzYlLUY5NictRiM2KUZqcEZdcUZjcUZdcUZmcUYyRkBGMkZALyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRjJGQEYyRkBGQkZaRmVzRmhvRl93LUY5NiUtRiM2KS1GZnI2JVEiM0YnRjJGQEZdcS1GZnI2JVEiMUYnRjJGQEZdcUZpcUYyRkBGMkZARkJGWi1GQzYwUSNpZkYnRl5wRjJGYHBGYnBGRkZJRktGTUZPRlFGU0ZkcEZlcEZfc0Zcci1GQzYuUSI9RidGMkZARkZGSUZLRk1GT0ZRRlNGVUZYRl9zRmd4Rl9zLUZDNjBRJXRoZW5GJ0ZecEYyRmBwRmJwRkZGSUZLRk1GT0ZRRlNGZHBGZXBGWkZfc0Zfc0Zfc0Zfc0ZbdEZoby1GLDYmUSVzb3J0RidGL0YyRjUtRjk2JS1GIzYsLUYsNiZRLUVpZ2VudmVjdG9yc0YnRi9GMkY1LUY5NiUtRiM2K0Zic0ZdcS1GLDYmUSdvdXRwdXRGJ0YvRjJGNUZdeS1GQzYuUSInRidGMkZARkZGSUZLRk1GT0ZRRlMvRlZRLDAuMTExMTExMWVtRidGZXAtRiw2JlElbGlzdEYnRi9GMkY1RmR6RjJGQEYyRkBGXXEtRjk2JS1GIzYnLUYsNiZRInhGJ0YvRjJGNUZdcS1GLDYmUSJ5RidGL0YyRjVGMkZARjJGQC1GQzYuUScmcmFycjtGJ0YyRkBGRkZJRktGTUZPRlFGU0ZkcEZlcC1JJW1zdWJHRiQ2JUZgW2wtRiM2JUZneEYyRkAvJS9zdWJzY3JpcHRzaGlmdEdGaHItRkM2LlElJmxlO0YnRjJGQEZGRklGS0ZNRk9GUUZTRlVGWC1GaltsNiVGY1tsRlxcbEZeXGxGMkZARjJGQEZCRlotRkM2MFElZWxpZkYnRl5wRjJGYHBGYnBGRkZJRktGTUZPRlFGU0ZkcEZlcEZfc0Zfc0ZcckZdeUZfcy1GQzYuUSomdW1pbnVzMDtGJ0YyRkBGRkZJRktGTUZPRlFGUy9GVlEsMC4yMjIyMjIyZW1GJy9GWUZcXWxGZ3hGX3NGYHlGWkZfc0Zfc0Zfc0Zfc0ZbdEZob0ZjeS1GOTYlLUYjNi1GaXItRiM2JkZqeUZdekYyRkBGaXJGXXFGXFtsRmZbbEZpW2wtRkM2LlEvJkdyZWF0ZXJFcXVhbDtGJ0YyRkBGRkZJRktGTUZPRlFGU0ZVRlhGY1xsRjJGQEYyRkBGQkZaLUZDNjBRJWVsc2VGJ0ZecEYyRmBwRmJwRkZGSUZLRk1GT0ZRRlNGZHBGZXBGX3NGWkZfc0Zfc0Zfc0ZbdEZob0ZqeS1GOTYlLUYjNipGYnNGXXFGYXpGXXlGZHpGaXpGZHpGQEYyRkBGQkZaLUZDNjBRI2ZpRidGXnBGMkZgcEZicEZGRklGS0ZNRk9GUUZTRmRwRmVwRkJGWkZaRl50RmhvLUYsNiZRI29wRidGL0YyRjUtRjk2JS1GIzYnRmd4Rl1xRlt0RjJGQEYyRkBGQkZhdEZob0ZhXmwtRjk2JS1GIzYnRmd4Rl1xRl50RjJGQEYyRkBGQkZkdEZob0ZhXmwtRjk2JS1GIzYnLUZmcjYlUSIyRidGMkZARl1xRl50RjJGQEYyRkBGQkZndEZob0ZhXmwtRjk2JS1GIzYpRmd4Rl1xRl9zRmFebC1GOTYlLUYjNidGZHhGXXFGXnRGMkZARjJGQEYyRkBGMkZARkJGWkZqdEZob0ZhXmwtRjk2JS1GIzYnRmBfbEZdcUZbdEYyRkBGMkZARkJGXXVGaG9GYV5sLUY5NiUtRiM2J0ZneEZdcUZqdEYyRkBGMkZARkJGYHVGaG9GYV5sLUY5NiUtRiM2J0ZgX2xGXXFGanRGMkZARjJGQEZCRmN1RmhvRmFebC1GOTYlLUYjNilGZ3hGXXFGX3NGYV5sLUY5NiUtRiM2J0ZkeEZdcUZqdEYyRkBGMkZARjJGQEYyRkBGQkZaRmZ1RmhvRmFebC1GOTYlLUYjNidGZHhGXXFGW3RGMkZARjJGQEZCRml1RmhvRmFebC1GOTYlLUYjNidGZ3hGXXFGZnVGMkZARjJGQEZCRlx2RmhvRmFebC1GOTYlLUYjNidGYF9sRl1xRmZ1RjJGQEYyRkBGQkZfdkZob0ZhXmwtRjk2JS1GIzYpRmd4Rl1xRl9zRmFebC1GOTYlLUYjNidGZHhGXXFGZnVGMkZARjJGQEYyRkBGMkZARkJGWkZidkZob0Zfdy1GOTYlLUYjNipGZHhGXXFGZHhGXXFGX3MtRjk2Jy1GIzYpRmd0Rl1xRmN1Rl1xRl92RjJGQEYyRkBGandGXXhGMkZARjJGQEZCRl9zRlpGZXZGaG8tRiw2JlEuTWF0cml4SW52ZXJzZUYnRi9GMkY1LUY5NiUtRiM2JUZidkYyRkBGMkZARkJGWkZodkZoby1GLDYmUSlNdWx0aXBseUYnRi9GMkY1LUY5NiUtRiM2KEZldkZdcUZiY2wtRjk2JS1GIzYnRmJzRl1xRmJ2RjJGQEYyRkBGMkZARjJGQEZCRlpGaHNGaG9GYmNsLUY5NiUtRiM2J0ZldkZdcUZlc0YyRkBGMkZARkItRmVuNiZGZ25Gam5GXW8vRmBvUSVhdXRvRidGWi1GLDYmUScmIzk0NTtGJ0Zed0YyRkBGaG8tRiw2JlEodW5hcHBseUYnRi9GMkY1LUY5NiUtRiM2KEZiY2wtRjk2JS1GIzYoRmJjbC1GOTYlLUYjNihGYnZGXXEtRiw2JlEyTWF0cml4RXhwb25lbnRpYWxGJ0YvRjJGNS1GOTYlLUYjNidGaHZGXXEtRiw2JlEidEYnRi9GMkY1RjJGQEYyRkBGMkZARjJGQEZdcUZoc0YyRkBGMkZARl1xRl5mbEYyRkBGMkZARkJGX3NGWkZaLUZDNi5RIiNGJ0YyRkBGRkZJRktGTUZPRlFGU0ZkcEZlcC1GLDYmUSZwcmludEYnRi9GMkY1LUY5NiUtRiM2KUZedEZdcUZqdEZdcUZmdUYyRkBGMkZALUZDNi5RIjtGJ0YyRkBGRkZgcUZLRk1GT0ZRRlNGZHBGWEZhZGxGWkZkZmwtRjk2JS1GIzYpRmF0Rl1xRmR0Rl1xRmd0RjJGQEYyRkBGW2dsRlpGYWRsRmRmbC1GOTYlLUYjNilGXXVGXXFGYHVGXXFGY3VGMkZARjJGQEZbZ2xGWkZkZmwtRjk2JS1GIzYpRml1Rl1xRlx2Rl1xRl92RjJGQEYyRkBGW2dsRlpGZGZsLUY5NiUtRiM2KC1GLDYmUSVgfkFgRidGL0YyRjVGXXlGX3NGYnNGMkZARjJGQEZbZ2xGWkZhZGxGZGZsLUY5NiUtRiM2Jy1GLDYmUSVgfktgRidGL0YyRjVGXXlGaHNGMkZARjJGQEZbZ2xGWkZhZGxGZGZsLUY5NiUtRiM2Jy1GLDYmUSVgflBgRidGL0YyRjVGXXlGYnZGMkZARjJGQEZbZ2xGWkZhZGxGZGZsLUY5NiUtRiM2K0Zfc0ZcaWwtRkM2LlEiXkYnRjJGQEZGRklGS0ZNRk9GUUZTRmd6L0ZZRmh6LUYsNiZRJWAtMWBGJ0YvRjJGNUZdeUZfc0ZldkYyRkBGMkZARltnbEZaRmRmbC1GOTYlLUYjNiktRiw2JlElYH5MYEYnRi9GMkY1Rl9zRl15Rl9zRmh2RjJGQEYyRkBGW2dsRlpGZGZsLUY5NiUtRiM2KS1GLDYmUStgfiZhbHBoYTtgRidGL0YyRjUtRjk2JS1GIzYlRl5mbEYyRkBGMkZARl15Rlt3RmhqbEYyRkBGMkZARltnbEZaRmRmbC1GOTYlLUYjNiktRiw2JlEsYH4mYWxwaGE7J2BGJ0YvRjJGNUZoamxGXXktRiw2JlElZGlmZkYnRi9GMkY1LUY5NiUtRiM2KEZbd0ZoamxGXXFGXmZsRjJGQEYyRkBGMkZARjJGQEZbZ2xGWkZhZGxGZGZsLUY5NiUtRiM2KS1GLDYmUSxgfkEmYWxwaGE7YEYnRi9GMkY1RmhqbEZdeUZiY2wtRjk2JS1GIzYoRmJzRl1xRlt3RmhqbEYyRkBGMkZARjJGQEYyRkBGW2dsRlpGYWRsRmRmbC1GOTYlLUYjNilGZWpsLUY5NiUtRiM2JUZlckYyRkBGMkZARl15Rlt3RmlcbUYyRkBGMkZARltnbEZfc0ZaLUYsNiZRJ1JFVFVSTkYnRi9GMkY1LUY5NiUtRiM2J0ZoZGwtRjk2JS1GIzYmLUY5NictRiM2LkZbdy1GOTYlLUYjNiRGXmZsRkBGMkZALUY5NictRiM2JkZneEZdcUZneEZARjJGQEZqd0ZdeEZdcUZbd0ZcXm0tRjk2Jy1GIzYmRmBfbEZdcUZneEZARjJGQEZqd0ZdeEZdcUZbd0ZcXm0tRjk2Jy1GIzYmRmR4Rl1xRmd4RkBGMkZARmp3Rl14RkBGMkZAL0ZbeFEzJkxlZnRBbmdsZUJyYWNrZXQ7RicvRl54UTQmUmlnaHRBbmdsZUJyYWNrZXQ7RidGXXFGXmZsRkBGMkZARmlyRjJGQEYyRkBGX3NGWkZfcy1GQzYwUSRlbmRGJ0ZecEYyRmBwRmJwRkZGSUZLRk1GT0ZRRlNGZHBGZXBGQkZpckZaRmFkbEZpci8lK2V4ZWN1dGFibGVHRkhGQA==JSFH
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-<Text-field style="Heading 1" layout="Heading 1">Flow Curve Code with P as Input</Text-field>
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-JSFH
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-<Text-field style="Heading 1" layout="Heading 1">Vector Calculus APIs </Text-field>
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-JSFH
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-<Text-field style="Heading 1" layout="Heading 1">Various Useful Examples</Text-field>
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-<Text-field bookmark="examples" style="Heading 2" layout="Heading 2">Examples-plots</Text-field>
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-Plot a sequence of related arrows.
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-Plot three points with various shapes.
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-Plot three points using various options.
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-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-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-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-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-Plot a sequence of arrows of differing sizes.
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-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-Display the eigenvectors of a given 3x3 matrix.
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-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-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-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-Produce a directional plot for a given vector-valued function.
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-LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictRiw2JVEmYXJyb3dGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUTAmQXBwbHlGdW5jdGlvbjtGJy9GOlEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkQvJSlzdHJldGNoeUdGRC8lKnN5bW1ldHJpY0dGRC8lKGxhcmdlb3BHRkQvJS5tb3ZhYmxlbGltaXRzR0ZELyUnYWNjZW50R0ZELyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGUy1JKG1mZW5jZWRHRiQ2JC1GIzYqLUZXNiYtRiM2J0YrLUYjNictRiw2JVEkc2VxRidGNkY5RjwtRlc2JC1GIzYpRistRiM2J0Zbb0Y8LUZXNiQtRiM2KC1GVzYmLUYjNictRlc2Ji1GIzYnLUYsNiVRImlGJ0Y2RjktRj02LVEiLEYnRkBGQi9GRkY4RkdGSUZLRk1GT0ZRL0ZVUSwwLjMzMzMzMzNlbUYnLUYsNiVRImpGJ0Y2RjkvJStleGVjdXRhYmxlR0ZERkBGQC8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0ZjcC1GVzYmLUYjNilGKy1GIzYnLUklbXN1cEdGJDYlLUY9Ni1RLyZFeHBvbmVudGlhbEU7RidGQEZCRkVGR0ZJRktGTUZPRlEvRlVRLDAuMTExMTExMWVtRidGYHAvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUY9Ni1RMSZJbnZpc2libGVUaW1lcztGJ0ZARkJGRUZHRklGS0ZNRk9GUUZULUYjNictRiw2JVEkc2luRicvRjdGREZARjwtRlc2JC1GIzYlRmBwRlxxRkBGQEZccUZARitGQEZjcC1GIzYnLUZbcjYlRl1yRmlwRmJyRmVyLUYjNictRiw2JVEkY29zRidGXXNGQEY8LUZXNiQtRiM2JUZpcEZccUZARkBGXHFGQEYrRkBGK0ZccUZARkBGXnFGYXFGXHFGQEZARl5xRmFxRmNwLUYjNihGYHAtRj02LVEiPUYnRkBGQkZFRkdGSUZLRk1GTy9GUlEsMC4yNzc3Nzc4ZW1GJy9GVUZldC1GIzYoRistRiM2Ji1GPTYtUSomdW1pbnVzMDtGJ0ZARkJGRUZHRklGS0ZNRk8vRlJRLDAuMjIyMjIyMmVtRicvRlVGX3UtSSNtbkdGJDYkUSI1RidGQEZccUZALUY9Ni1RIy4uRidGQEZCRkVGR0ZJRktGTUZPRl51RlRGYXVGXHFGQEYrRlxxRkBGK0ZccUZARkBGXHFGQEZjcC1GIzYoRmlwRmF0Rmd0RitGXHFGQEYrRlxxRkBGQEZccUZARitGXHFGQEZAL0ZfcVEifGZyRicvRmJxUSJ8aHJGJ0ZjcC1GIzYnLUYsNiVRJ2xlbmd0aEYnRjZGOUZhdC1GYnU2JFEkMC40RidGQEZccUZARmNwLUYjNictRiw2JVEoc2NhbGluZ0YnRjZGOUZhdC1GLDYlUSxjb25zdHJhaW5lZEYnRjZGOUZccUZARitGXHFGQEZARlxxRkBGK0ZccUZARitGXHFGQA==
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-Display triads at a number of points.
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-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-<Text-field bookmark="examples" style="Heading 2" layout="Heading 2">Examples-plots/plottools</Text-field>
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-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-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-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-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-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-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-LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
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-<Text-field bookmark="examples" style="Heading 2" layout="Heading 2">Examples-map</Text-field>
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-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-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-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-map(proc(x,y) x^2+y end proc, [1,2,3,4], 2);
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-LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictRiw2JVElbWFwMkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMCZBcHBseUZ1bmN0aW9uO0YnL0Y6USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRC8lKXN0cmV0Y2h5R0ZELyUqc3ltbWV0cmljR0ZELyUobGFyZ2VvcEdGRC8lLm1vdmFibGVsaW1pdHNHRkQvJSdhY2NlbnRHRkQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZTLUkobWZlbmNlZEdGJDYkLUYjNiktRiw2JVEiZkYnRjZGOS1GPTYtUSIsRidGQEZCL0ZGRjhGR0ZJRktGTUZPRlEvRlVRLDAuMzMzMzMzM2VtRictRiw2JVEiZ0YnRjZGOUZobi1GVzYmLUYjNiktRiw2JVEiYUYnRjZGOUZobi1GLDYlUSJiRidGNkY5RmhuLUYsNiVRImNGJ0Y2RjkvJStleGVjdXRhYmxlR0ZERkBGQC8lJW9wZW5HUSJ8ZnJGJy8lJmNsb3NlR1EifGhyRidGXnBGQEZARl5wRkBGK0ZecEZARitGXnBGQA==
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-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-The following example counts the number of finite Abelian groups of the order n by using the map and map2 commands.
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-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-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
-
-
-
-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
-
-
-
-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
-
-The map command can be used with type atomic.
-
-sum_to_product:=proc(expr)
- if expr::atomic then
- expr;
- elif expr::`+` then
- `*`(op(expr));
- else
- map(procname,expr); end if;
-end proc:
-
-
-
-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
-
-
-
-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
-
-
-
-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
-
-
-
-LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1JJW1zdWJHRiQ2JS1GLDYlUSJBRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiUtSSNtbkdGJDYkUSIxRicvRjtRJ25vcm1hbEYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRidGQy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRkVGQ0YrRkVGQw==
-
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-
-LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
-
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-
-
-
-
-LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
-
-
-
\ No newline at end of file
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diff --git a/LinearCompartmentModels.mw b/LinearCompartmentModels.mw
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@@ -0,0 +1,1443 @@
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+
+Linear Compartment Models in Engineering & Medicine
+Dr. John Pais
+
+
+
+Ladue Horton Watkins
+
+
+
+pais.john@gmail.com
+
+
+
+
+
+
+
+LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
+
+
+<Text-field style="Heading 1" layout="Heading 1">3x3 Eigenvalue & Eigenvector Examples: Flow Curves for Dynamical Systems </Text-field>
+
+Example 1. Real Distinct Eigenvalues
+
+
+
+Enter the three rows of the matrix A and the initialization vector.
+Click anywhere into the math area below and press [Enter].
+
+
+
+LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUkjbWlHRiQ2JlEoJmFscGhhO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lMGZvbnRfc3R5bGVfbmFtZUdRKTJEfklucHV0RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LlEqJmNvbG9uZXE7RidGMkY1LyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYmUS5mbG93Q3VydmVQbHVzRicvRjBRJXRydWVGJ0YyL0Y2USdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JS1GIzYrLUZXNictRiM2KC1JI21uR0YkNiVRIjRGJ0YyRjUtRjk2LlEiLEYnRjJGNUY8L0Y/RlNGQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZOUSwwLjMzMzMzMzNlbUYnLUZqbjYlUSIwRidGMkY1Rl1vLUZqbjYlUSIxRidGMkY1RjVGMkY1LyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRl1vLUZXNictRiM2KS1GOTYuUSomdW1pbnVzMDtGJ0YyRjVGPEY+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZpcC1Gam42JVEiMkYnRjJGNUZdb0Zob0Zdb0Zlb0Y1RjJGNUZbcEZecEZdby1GVzYnLUYjNilGZXBGW3FGXW9GZW9GXW9GaG9GNUYyRjVGW3BGXnBGXW8tRlc2Jy1GIzYoRmluRl1vLUZqbjYlUSI4RidGMkY1Rl1vLUZqbjYlUSMxMkYnRjJGNUY1RjJGNUZbcEZecC1GLDYjUSFGJ0Y1RjJGNS1GOTYuUSI6RidGMkY1RjxGPkZARkJGREZGRkhGSkZNLUY5Ni5RIn5GJ0YyRjVGPEY+RkBGQkZERkZGSEZhby9GTkZib0Zici8lK2V4ZWN1dGFibGVHRjFGNQ==
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+
+Example 1. Real Distinct Eigenvalues (continued)
+
+
+
+Using the P matrix you computed by hand.
+Enter the three rows of the matrix A, the initialization vector, and the three rows of your P matrix.
+Click anywhere into the math area below and press [Enter].
+
+
+
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+LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
+
+
+
+JSFH
+
+
+
+Example 2. Real Distinct Eigenvalues
+
+
+
+Enter the three rows of the matrix A and the initialization vector.
+Click anywhere into the math area below and press [Enter].
+
+
+
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
+
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+
+JSFH
+
+
+
+Example 2. Real Distinct Eigenvalues (continued)
+
+
+
+Using the P matrix you computed by hand.
+Enter the three rows of the matrix A, the initialization vector, and the three rows of your P matrix.
+Click anywhere into the math area below and press [Enter].
+
+
+
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
+
+
+
+
+
+
+
+
+
+
+
+
+
+LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
+
+
+
+JSFH
+
+
+
+Example 3. Real Distinct Eigenvalues
+
+
+
+Enter the three rows of the matrix A and the initialization vector.
+Click anywhere into the math area below and press [Enter].
+
+
+
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
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
+
+
+
+Example 3. Real Distinct Eigenvalues (continued)
+
+
+
+Using the P matrix you computed by hand.
+Enter the three rows of the matrix A, the initialization vector, and the three rows of your P matrix.
+Click anywhere into the math area below and press [Enter].
+
+
+
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
+
+
+
+
+
+
+
+JSFH
+
+
+
+Example 4. Complex Eigenvalues
+
+
+
+Enter the three rows of the matrix A and the initialization vector.
+Click anywhere into the math area below and press [Enter].
+
+
+
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
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+JSFH
+
+
+
+Example 4. Complex Eigenvalues (continued)
+
+
+
+Using the P matrix you computed by hand.
+Enter the three rows of the matrix A, the initialization vector, and the three rows of your P matrix.
+Click anywhere into the math area below and press [Enter].
+
+
+
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
+
+
+
+
+
+
+
+JSFH
+
+
+
+Example 5. Complex Eigenvalues
+
+
+
+Enter the three rows of the matrix A and the initialization vector.
+Click anywhere into the math area below and press [Enter].
+
+
+
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
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Example 5. Complex Eigenvalues (continued)
+
+
+
+Using the P matrix you computed by hand.
+Enter the three rows of the matrix A, the initialization vector, and the three rows of your P matrix.
+Click anywhere into the math area below and press [Enter].
+
+
+
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
+
+
+
+
+
+
+
+JSFH
+
+
+
+Example 6. Complex Eigenvalues
+
+
+
+Enter the three rows of the matrix A and the initialization vector.
+Click anywhere into the math area below and press [Enter].
+
+
+
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
+
+
+
+
+
+
+
+JSFH
+
+
+
+Example 6. Complex Eigenvalues (continued)
+
+
+
+Using the P matrix you computed by hand.
+Enter the three rows of the matrix A, the initialization vector, and the three rows of your P matrix.
+Click anywhere into the math area below and press [Enter].
+
+
+
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
+
+
+
+
+
+
+
+JSFH
+
+
+
+Example 7. Real Repeated Eigenvalues
+
+
+
+Enter the three rows of the matrix A and the initialization vector.
+Click anywhere into the math area below and press [Enter].
+
+
+
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
+
+
+
+LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
+
+
+
+
+
+
+
+JSFH
+
+
+
+Example 7. Real Repeated Eigenvalues (continued)
+
+
+
+Using the P matrix you computed by hand.
+Enter the three rows of the matrix A, the initialization vector, and the three rows of your P matrix.
+Click anywhere into the math area below and press [Enter].
+
+
+
+LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JlEoJmFscGhhO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lMGZvbnRfc3R5bGVfbmFtZUdRKTJEfklucHV0RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LlEqJmNvbG9uZXE7RidGMkY1LyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYmUTBmbG93Q3VydmVJbnB1dFBGJy9GMFEldHJ1ZUYnRjIvRjZRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNi4tRiw2I1EhRictRiM2JkZlbi1GIzYoLUZXNictRiM2KC1JJm1mcmFjR0YkNigtSSNtbkdGJDYlUSIxRidGMkY1LUYjNiQtRmRvNiVRIjJGJ0YyRjVGNS8lLmxpbmV0aGlja25lc3NHRmZvLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmBwLyUpYmV2ZWxsZWRHRjEtRjk2LlEiLEYnRjJGNUY8L0Y/RlNGQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZOUSwwLjMzMzMzMzNlbUYnLUZkbzYlUSIwRidGMkY1RmVwRmBvRjVGMkY1LyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRmVwLUZXNictRiM2KEZdcUZlcEZjb0ZlcEZdcUY1RjJGNUZgcUZjcUZlcC1GVzYnLUYjNiktRmFvNigtRmRvNiVRIjNGJ0YyRjVGZ29GXHBGXnBGYXBGY3BGZXBGXXFGZXAtRjk2LlEqJnVtaW51czA7RidGMkY1RjxGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GZ3JGYG9GNUYyRjVGYHFGY3FGNUZlbkY1RmVuRmVwLUZXNictRiM2KC1GZG82JVEiNEYnRjJGNUZlcC1GZG82JVEiOEYnRjJGNUZlcC1GZG82JVEjMTJGJ0YyRjVGNUYyRjVGYHFGY3FGZXAtRlc2Jy1GIzYpRmNyLUZhbzYoRmNvLUYjNiZGYHJGUkYyRlRGXHBGXnBGYXBGY3BGZXBGY29GZXBGXXFGNUYyRjVGYHFGY3FGZXAtRlc2Jy1GIzYoRl1xRmVwRl1xRmVwRmNvRjVGMkY1RmBxRmNxRmVwLUZXNictRiM2KEZdcUZlcEZjb0ZlcEZjb0Y1RjJGNUZgcUZjcUY1RjJGNS1GOTYtUSI6RidGNUY8Rj5GQEZCRkRGRkZIRkpGTS8lK2V4ZWN1dGFibGVHRjFGNQ==
+
+
+
+
+
+
+
+JSFH
+
+
+
+Example 8. Real Repeated Eigenvalues
+
+
+
+Enter the three rows of the matrix A and the initialization vector.
+Click anywhere into the math area below and press [Enter].
+
+
+
+LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUkjbWlHRiQ2JlEoJmFscGhhO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lMGZvbnRfc3R5bGVfbmFtZUdRKTJEfklucHV0RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LlEqJmNvbG9uZXE7RidGMkY1LyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYmUS5mbG93Q3VydmVQbHVzRicvRjBRJXRydWVGJ0YyL0Y2USdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JS1GIzYoLUYsNiNRIUYnLUYjNidGZW4tRiM2KS1GVzYnLUYjNiotSSNtbkdGJDYlUSIzRidGMkY1LUY5Ni5RIixGJ0YyRjVGPC9GP0ZTRkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTlEsMC4zMzMzMzMzZW1GJy1GOTYuUSomdW1pbnVzMDtGJ0YyRjVGPEY+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZgcC1GYW82JVEiMUYnRjJGNUZkby1GYW82JVEiMkYnRjJGNUYyRjVGMkY1LyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRmRvLUZXNictRiM2KkZgb0Zkb0ZccEZicEZkby1GYW82JVEiNkYnRjJGNUYyRjVGMkY1RmhwRltxRmRvLUZXNictRiM2K0ZccEZlcEZkb0ZlcEZkb0ZccEZlcEYyRjVGMkY1RmhwRltxRjJGNUZlbkYyRjVGZW5GZG8tRlc2Jy1GIzYoLUZhbzYlUSI0RidGMkY1RmRvLUZhbzYlUSI4RidGMkY1RmRvLUZhbzYlUSMxMkYnRjJGNUY1RjJGNUZocEZbcUY1RjJGNS1GOTYuUSI6RidGMkY1RjxGPkZARkJGREZGRkhGSkZNLUY5Ni5RIn5GJ0YyRjVGPEY+RkBGQkZERkZGSEZoby9GTkZpb0Zpci8lK2V4ZWN1dGFibGVHRjFGNQ==
+
+
+
+
+
+
+
+
+
+
+
+Example 8. Real Repeated Eigenvalues (continued)
+
+
+
+Using the P matrix you computed by hand.
+Enter the three rows of the matrix A, the initialization vector, and the three rows of your P matrix.
+Click anywhere into the math area below and press [Enter].
+
+
+
+LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JlEoJmFscGhhO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lMGZvbnRfc3R5bGVfbmFtZUdRKTJEfklucHV0RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LlEqJmNvbG9uZXE7RidGMkY1LyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYmUTBmbG93Q3VydmVJbnB1dFBGJy9GMFEldHJ1ZUYnRjIvRjZRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNi4tRiw2I1EhRictRiM2J0Zlbi1GIzYpLUZXNictRiM2Ki1JI21uR0YkNiVRIjNGJ0YyRjUtRjk2LlEiLEYnRjJGNUY8L0Y/RlNGQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZOUSwwLjMzMzMzMzNlbUYnLUY5Ni5RKiZ1bWludXMwO0YnRjJGNUY8Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZORmBwLUZhbzYlUSIxRidGMkY1RmRvLUZhbzYlUSIyRidGMkY1RjJGNUYyRjUvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGZG8tRlc2Jy1GIzYqRmBvRmRvRlxwRmJwRmRvLUZhbzYlUSI2RidGMkY1RjJGNUYyRjVGaHBGW3FGZG8tRlc2Jy1GIzYrRlxwRmVwRmRvRmVwRmRvRlxwRmVwRjJGNUYyRjVGaHBGW3FGMkY1RmVuRjJGNUZlbkZkby1GVzYnLUYjNigtRmFvNiVRIjRGJ0YyRjVGZG8tRmFvNiVRIjhGJ0YyRjVGZG8tRmFvNiVRIzEyRidGMkY1RjVGMkY1RmhwRltxRmRvLUZXNictRiM2KkZccC1JJm1mcmFjR0YkNihGYnAtRiM2JEZlcEY1LyUubGluZXRoaWNrbmVzc0dGZHAvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGY3MvJSliZXZlbGxlZEdGMUZkb0ZicEZkb0ZccEZlcEY1RjJGNUZocEZbcUZkby1GVzYnLUYjNilGXHAtRltzNihGYG8tRiM2JkZlcEZSRjJGVEZfc0Zhc0Zkc0Zmc0Zkb0ZicEZkby1GYW82JVEiMEYnRjJGNUY1RjJGNUZocEZbcUZkby1GVzYnLUYjNihGYnBGZG9GYHRGZG9GYnBGNUYyRjVGaHBGW3FGNUYyRjUtRjk2LVEiOkYnRjVGPEY+RkBGQkZERkZGSEZKRk0vJStleGVjdXRhYmxlR0YxRjU=
+
+
+
+
+
+
+
+JSFH
+
+
+
+Example 9. Real Repeated Eigenvalues
+
+
+
+Hirsch and Smale Example 2, p. 112. Check new flowCurvePlus with one Eigenvalue with multiplicity 2 but S + N needed
+since only one basis eigenvector, thus must find the kernel of Caley-Hamilton power operator for the basis.
+Click anywhere into the math area below and press [Enter].
+
+
+
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
+
+
+
+
+
+
+
+
+
+
+
+Example 9. Real Repeated Eigenvalues (continued)
+
+
+
+Using the P matrix you computed by hand.
+Enter the three rows of the matrix A, the initialization vector, and the three rows of your P matrix.
+Click anywhere into the math area below and press [Enter].
+
+
+
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
+
+
+
+
+
+
+
+JSFH
+
+
+
+Example 10. Real Repeated Eigenvalues
+
+
+
+Enter the three rows of the matrix A and the initialization vector.
+Click anywhere into the math area below and press [Enter].
+
+
+
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
+
+
+
+
+
+
+
+LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
+
+
+
+Example 10. Real Repeated Eigenvalues (continued)
+
+
+
+Using the P matrix you computed by hand.
+Enter the three rows of the matrix A, the initialization vector, and the three rows of your P matrix.
+Click anywhere into the math area below and press [Enter].
+
+
+
+LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JlEoJmFscGhhO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lMGZvbnRfc3R5bGVfbmFtZUdRKTJEfklucHV0RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LlEqJmNvbG9uZXE7RidGMkY1LyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYmUTBmbG93Q3VydmVJbnB1dFBGJy9GMFEldHJ1ZUYnRjIvRjZRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNi4tRiw2I1EhRictRiM2J0Zlbi1GIzYnRmVuLUYjNiktRlc2Jy1GIzYqLUY5Ni5RKiZ1bWludXMwO0YnRjJGNUY8Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZORmZvLUkjbW5HRiQ2JVEiM0YnRjJGNS1GOTYuUSIsRidGMkY1RjwvRj9GU0ZARkJGREZGRkgvRktRJjAuMGVtRicvRk5RLDAuMzMzMzMzM2VtRictRmlvNiVRIjBGJ0YyRjVGXHBGZHBGMkY1RjJGNS8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0ZccC1GVzYnLUYjNipGZHBGXHBGYm9GaG9GXHBGZHBGMkY1RjJGNUZncEZqcEZccC1GVzYnLUYjNipGZHBGXHBGZHBGXHBGYm9GaG9GMkY1RjJGNUZncEZqcEYyRjVGZW5GMkY1RmVuRjJGNUZlbkZccC1GVzYnLUYjNigtRmlvNiVRIjRGJ0YyRjVGXHAtRmlvNiVRIjhGJ0YyRjVGXHAtRmlvNiVRIzEyRidGMkY1RjVGMkY1RmdwRmpwRlxwLUZXNictRiM2KEZkcEZccEZkcEZccC1GaW82JVEiMUYnRjJGNUY1RjJGNUZncEZqcEZccC1GVzYnLUYjNihGZHBGXHBGZnJGXHBGZHBGNUYyRjVGZ3BGanBGXHAtRlc2Jy1GIzYoRmZyRlxwRmRwRlxwRmRwRjVGMkY1RmdwRmpwRjVGMkY1LUY5Ni1RIjpGJ0Y1RjxGPkZARkJGREZGRkhGSkZNLyUrZXhlY3V0YWJsZUdGMUY1
+
+
+
+
+
+
+
+JSFH
+
+
+
+Linear Compartment Model: Recall our previous Brine Tank (used in water softeners) Cascade Problem for an Open System
+
+
+
+
+
+
+
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LSUrQU5OT1RBVElPTkc2Jy0lKUJPVU5EU19YRzYjJCIiISEiIi0lKUJPVU5EU19ZR0YnLSUtQk9VTkRTX1dJRFRIRzYjJCIlIVEpRiotJS5CT1VORFNfSEVJR0hURzYjJCIlcUtGKi0lKUNISUxEUkVORzYi
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+JSFH
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+Brine Tank Cascade Problem 1. Real Distinct Eigenvalues
+Enter the three rows of the matrix A and the initialization vector.
+Click anywhere into the math area below and press [Enter].
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+
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+LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
+
+
+
+Brine Tank Cascade Problem 1. Real Distinct Eigenvalues (continued)
+
+
+
+
+
+
+
+Using the P matrix you computed by hand.
+
+
+
+
+Enter the three rows of the matrix A, the initialization vector, and the three rows of your P matrix.
+Click anywhere into the math area below and press [Enter].
+
+
+
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
+
+
+
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
+
+
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+LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
+
+
+
+JSFH
+
+
+
+Linear Compartment Model: Brine Tank Cascade Problem for a Closed System
+
+
+
+
+
+
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LSUrQU5OT1RBVElPTkc2Jy0lKUJPVU5EU19YRzYjJCIiISEiIi0lKUJPVU5EU19ZR0YnLSUtQk9VTkRTX1dJRFRIRzYjJCIlIVEpRiotJS5CT1VORFNfSEVJR0hURzYjJCIlP0tGKi0lKUNISUxEUkVORzYi
+
+
+
+Brine Tank Cascade Problem 2. Complex Eigenvalues
+Enter the three rows of the matrix A and the initialization vector.
+Click anywhere into the math area below and press [Enter].
+
+
+
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
+
+
+
+JSFHJSFH
+
+
+
+JSFH
+
+
+
+Brine Tank Cascade Problem 2. Complex Eigenvalues (continued)
+
+
+
+
+
+
+
+Using the P matrix you computed by hand.
+
+
+
+
+Enter the three rows of the matrix A, the initialization vector, and the three rows of your P matrix.
+Click anywhere into the math area below and press [Enter].
+
+
+
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
+
+
+
+
+
+
+
+JSFH
+
+
+
+Brine Tank Cascade Problem 3. Complex Eigenvalues
+Enter the three rows of the matrix A and the initialization vector.
+Click anywhere into the math area below and press [Enter].
+
+
+
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+
+
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+LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
+
+
+
+LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
+
+
+
+Brine Tank Cascade Problem 3. Complex Eigenvalues (continued)
+
+
+
+
+
+
+
+Using the P matrix you computed by hand.
+
+
+
+
+Enter the three rows of the matrix A, the initialization vector, and the three rows of your P matrix.
+Click anywhere into the math area below and press [Enter].
+
+
+
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
+
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+JSFH
+
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+
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+
+<Text-field style="Heading 1" layout="Heading 1">3x3 Eigenvalue & Eigenvector Examples: Flow Curves for Drug Absorption Model Dynamical Systems</Text-field>
+
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LSUrQU5OT1RBVElPTkc2Jy0lKUJPVU5EU19YRzYjJCIjNSEiIi0lKUJPVU5EU19ZRzYjJCIiIUYqLSUtQk9VTkRTX1dJRFRIRzYjJCIlIUgoRiotJS5CT1VORFNfSEVJR0hURzYjJCIlNVFGKi0lKUNISUxEUkVORzYi
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+Click on the edge of the image below to see vcr controls (in the task bar above) to run the animation.
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+Drug Absorption Model Linear Solution Functions: General Percent Concentration Functions
+Click anywhere into the math area below and press [Enter].
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
+
+
+
+
+
+
+
+Drug Absorption Model Linear Solution Functions: Specific Percent Concentration Functions for start values of the animation above.
+Click anywhere into the math area below and press [Enter].
+
+
+
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+Note that these Linear Solution Functions above can be found by soving the eigenvalue problem immediately below:
+
+
+
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
+
+
+
+Absorption Model Problem 1. Real Distinct Eigenvalues
+Enter the three rows of the matrix A and the initialization vector.
+Click anywhere into the math area below and press [Enter].
+
+
+
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+<Text-field style="Heading 1" layout="Heading 1">Drug Absorption Model</Text-field><Text-field style="Normal" layout="Normal">Define general model for first-order absorption with metabolite concentration, which specializes</Text-field><Text-field style="Normal" layout="Normal">to the first-order absorption model with metabolite elimination when k4 = 0, and to the standard
+first-order absorption model when k3 = k4 = 0.</Text-field>
+
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+<Text-field style="Heading 1" layout="Heading 1">Flow Curve Plus Code</Text-field>
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2MFEkZW5kRidGXnBGMkZgcEZicEZGRklGS0ZNRk9GUUZTRmRwRmVwRkJGWkZfekZcckZfXGxGQA==
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+<Text-field style="Heading 1" layout="Heading 1">Flow Curve Code</Text-field>
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JSFH
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+<Text-field style="Heading 1" layout="Heading 1">Flow Curve Code with P as Input</Text-field>
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+<Text-field style="Heading 1" layout="Heading 1">Vector Calculus APIs </Text-field>
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+JSFH
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+<Text-field style="Heading 2" family="Arial" layout="Heading 2"><Font family="Arial">Background</Font></Text-field>
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+The classical SIR model assumes that a population can be divided into three distinct compartments (see e.g. Bloomfiled[2009, pp 149]): S is the proportion of susceptibles, I is the proportion of infected persons and R is the proportion of persons that have recovered from infection and are now immune against the disease. This model was originally developed in 1927 by Kermack and McKendrik.
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+JSFH
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+
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LSUrQU5OT1RBVElPTkc2Jy0lKUJPVU5EU19YRzYjJCIjNSEiIi0lKUJPVU5EU19ZRzYjJCIiIUYqLSUtQk9VTkRTX1dJRFRIRzYjJCIlXURGKi0lLkJPVU5EU19IRUlHSFRHNiMkIiRxJkYqLSUpQ0hJTERSRU5HNiI=
+
+
+
+ Figure 1
+
+
+
+
+
+
+
+The classic SIR model can be described by three functions:
+
+
+
+
+
+
+
+The basic reproduction ratio LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGNC8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRi82I1EhRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y6RjVGNw==, for the classic SIR model as defined above, can be derived as:
+
+
+
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+LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGNC8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRi82I1EhRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIn5GJ0Y1RjcvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZURjVGNw== is the number of secondary infections that is produced by one primary infection in a wholly susceptible population. Only when LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGNC8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRi82I1EhRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIn5GJ0Y1RjcvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZURjVGNw== > 1, does an epidemic occurs. 1/\316\263 is the average infectious period. Setting equations (1)-(3) equal to zero and solving these for the equilibrium solutions of 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 and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtRiw2JlEidEYnRi9GMkY1RjIvRjZRJ25vcm1hbEYnRjJGQC1GLDYjUSFGJ0YyRkA= yields an equilibrium whenever LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRInRGJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGQC1JI21vR0YkNi1RIj1GJ0ZALyUmZmVuY2VHRj8vJSpzZXBhcmF0b3JHRj8vJSlzdHJldGNoeUdGPy8lKnN5bW1ldHJpY0dGPy8lKGxhcmdlb3BHRj8vJS5tb3ZhYmxlbGltaXRzR0Y/LyUnYWNjZW50R0Y/LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGVi1JI21uR0YkNiRRIzAuRidGQEY9RkA=
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+Notes: (1) The basic reproduction ratio LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GLzYjUSFGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEifkYnRjUvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZSLyUrZXhlY3V0YWJsZUdGNEY1is often ambiguously denoted LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYsNiZRIjBGJ0YvRjJGNS8lL3N1YnNjcmlwdHNoaWZ0R0Y6, leading to potential confusion with LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiQtSSNtbkdGJDYlUSIwRidGMi9GNlEnbm9ybWFsRidGQUYyRkFGQQ==, which is the initial value of the recovered function LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiQtRiw2JlEidEYnRi9GMkY1L0Y2USdub3JtYWxGJ0YyRkBGQA==. (2) Not all combinations of infection and removal rates within the ranges of the interactive model below will match a real existing infectious disease. (3)The SIR model exists in different flavors and parametrizations, the model as presented here follows Bloomfield[2009].
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+<Text-field style="Heading 2" layout="Heading 2"><Font family="Arial">Interactive SIR model: Infectious Disease Nonlinear Compartment Model 1</Font></Text-field>
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+LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
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+<Text-field style="Heading 2" family="Arial" layout="Heading 2"><Font family="Arial">Background</Font></Text-field>
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+The classical SIR model assumes that a population can be divided into three distinct compartments (see e.g. Bloomfield[2009, pp 149]): S is the proportion of susceptibles, I is the proportion of infected persons and R is the proportion of persons that have recovered from infection and are now immune against the disease. This model was originally developed in 1927 by Kermack and McKendrik.
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+One extension to the classic SIR model is to add births and deaths to the model. Thus there is an inflow of new susceptibles and an outflow from all three compartments. In its simplest form, the birth rate is set equal to the death rate which is assumed not to be related to the infectious disease.
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LSUrQU5OT1RBVElPTkc2Jy0lKUJPVU5EU19YRzYjJCIjNSEiIi0lKUJPVU5EU19ZRzYjJCIiIUYqLSUtQk9VTkRTX1dJRFRIRzYjJCIlIXAjRiotJS5CT1VORFNfSEVJR0hURzYjJCIkISoqRiotJSlDSElMRFJFTkc2Ig==
+
+
+ Figure 1
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+
+
+
+
+
+
+The extended SIR model with births and deaths can be described by three functions:
+
+
+
+
+
+
+
+The basic reproduction ratio LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGNC8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRi82I1EhRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y6RjVGNw==, for the SIR model as defined above, can be derived as:
+
+
+
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
+
+
+
+
+
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+LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGNC8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRi82I1EhRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIn5GJ0Y1RjcvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZURjVGNw== is the number of secondary infections that is produced by one primary infection in a wholly susceptible population. Only when LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGNC8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRi82I1EhRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIn5GJ0Y1RjcvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZURjVGNw== > 1, does an epidemic occurs. 1/(\316\263+\316\274) is the average infectious period. Setting equations (1)-(3) equal to zero and solving these for the equilibrium solutions of 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 and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtRiw2JlEidEYnRi9GMkY1RjIvRjZRJ25vcm1hbEYnRjJGQC1GLDYjUSFGJ0YyRkA= in dependence of the parameters LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JlEnJiM5NTY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYuUSIsRidGMkY0LyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRjg2LlEifkYnRjJGNEY7L0Y+RjFGQEZCRkRGRkZIRkovRk5GTC1GLDYmUScmIzk0NjtGJ0YvRjJGNEY3RjJGNA==and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEnJiM5NDc7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYuUSJ+RidGMkY0LyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGS0Y3RjJGNA==(e.g. by using the Maple procedure solve()) provides the following equilibrium solution:
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+Notes: (1) The basic reproduction ratio LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GLzYjUSFGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEifkYnRjUvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZSLyUrZXhlY3V0YWJsZUdGNEY1is often ambiguously denoted LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYsNiZRIjBGJ0YvRjJGNS8lL3N1YnNjcmlwdHNoaWZ0R0Y6, leading to potential confusion with LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiQtSSNtbkdGJDYlUSIwRidGMi9GNlEnbm9ybWFsRidGQUYyRkFGQQ==, which is the initial value of the recovered function LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiQtRiw2JlEidEYnRi9GMkY1L0Y2USdub3JtYWxGJ0YyRkBGQA==. (2) Not all combinations of infection and removal rates within the ranges of the interactive model below will match a real existing infectious disease. (3)The SIR model exists in different flavors and parametrizations, the model as presented here follows Bloomfield[2009].
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+<Text-field style="Heading 2" layout="Heading 2"><Font family="Arial">Interactive Extended SIR model: Infectious Disease Nonlinear Compartment Model 2</Font></Text-field>
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+LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
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+<Text-field style="Heading 2" family="Arial" layout="Heading 2"><Font family="Arial">Background</Font></Text-field>
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+The SEIR model is an extension of the classical SIR (Susceptibles, Infected, Recovered) model which was originally developed by Kermack/McKendrick[1927]: a fourth compartment is added which contains exposed persons which are infected but are not yet infectious. The SEIR (Susceptibles, Exposed, Infectious, Recovered) model as presented here covers also births and deaths. Persons in all compartments are measured as fractions of the total population. The birth rate is set equal to the death rate which is assumed not to be related to the infectious disease. It can be shown that the inverse of the death rate is equal to the life expectancy.
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LSUrQU5OT1RBVElPTkc2Jy0lKUJPVU5EU19YRzYjJCIjNSEiIi0lKUJPVU5EU19ZRzYjJCIiIUYqLSUtQk9VTkRTX1dJRFRIRzYjJCIlK01GKi0lLkJPVU5EU19IRUlHSFRHNiMkIiQhKipGKi0lKUNISUxEUkVORzYi
+
+
+ Figure 1
+
+
+
+
+
+
+
+The extended SEIR model with births and deaths can be described by four functions:
+
+
+
+
+
+
+
+The basic reproduction ratio LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEnJiM5NjE7RicvJSdmYW1pbHlHUSZBcmlhbEYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRi82I1EhRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y7RjIvJStleGVjdXRhYmxlR0Y3Rjg=, for the SIR model as defined above, can be derived as:
+
+
+
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+LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GLzYjUSFGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEifkYnRjUvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZSLyUrZXhlY3V0YWJsZUdGNEY1 is the number of secondary infections that is produced by one primary infection in a wholly susceptible population. Only when LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GLzYjUSFGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEifkYnRjUvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZSLyUrZXhlY3V0YWJsZUdGNEY1 > 1, does an epidemic occurs. 1/(\316\263+\316\274) is the average infectious period. Setting equations (1)-(4) equal to zero and solving these for the equilibrium solutions of 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, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiRUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiQtRiw2JlEidEYnRi9GMkY1L0Y2USdub3JtYWxGJ0YyRkBGQA== and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRInRGJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGQC1GLDYjUSFGJ0Y9RkA= in dependence of the parameters 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 and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEnJiM5NDc7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIn5GJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGSUY1LyUrZXhlY3V0YWJsZUdGMUYy(e.g. by using the Maple procedure solve()) provides the following equilibrium solution:JSFH
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+Notes: (1) The basic reproduction ratio LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GLzYjUSFGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEifkYnRjUvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZSLyUrZXhlY3V0YWJsZUdGNEY1is often ambiguously denoted LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYsNiZRIjBGJ0YvRjJGNS8lL3N1YnNjcmlwdHNoaWZ0R0Y6, leading to potential confusion with LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiQtSSNtbkdGJDYlUSIwRidGMi9GNlEnbm9ybWFsRidGQUYyRkFGQQ==, which is the initial value of the recovered function LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiQtRiw2JlEidEYnRi9GMkY1L0Y2USdub3JtYWxGJ0YyRkBGQA==. (2) Not all combinations of infection and removal rates within the ranges of the interactive model below will match a real existing infectious disease. (3) The SEIR model exists in different flavors and parametrizations, the model as presented here follows Keeling/Rohani[2008].
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+<Text-field style="Heading 2" layout="Heading 2"><Font family="Arial">Interactive SEIR model: Infectious Disease Nonlinear Compartment Model 3</Font></Text-field>