Last change 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G\303\274nter Edenharter\302\251 edenharter researchEducational revision 2020/03/15
JSFH<Text-field style="Heading 2" family="Arial" layout="Heading 2"><Font family="Arial">Background</Font></Text-field>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 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Figure 1The extended SEIR model with births and deaths can be described by four functions:
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiU0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtRiw2JlEidEYnRi9GMkY1RjIvRjZRJ25vcm1hbEYnRjJGQEYyRkA=:fraction of susceptiblesLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiRUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtRiw2JlEidEYnRi9GMkY1RjIvRjZRJ25vcm1hbEYnRjJGQEYyRkA=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LlEiOkYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGRUYvRjI=fraction of exposed personsLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtRiw2JlEidEYnRi9GMkY1RjIvRjZRJ25vcm1hbEYnRjJGQEYyRkA=:fraction of infectious personsLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtRiw2JlEidEYnRi9GMkY1RjIvRjZRJ25vcm1hbEYnRjJGQEYyRkA=:fraction of recovered persons
parameters:
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0:birth and death rate, 1/\316\274=life 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0:infection 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0:exposed (infected) to infectious 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0:removal rateLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lK2V4ZWN1dGFibGVHRjFGMg==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEiPkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv0:basic reproduction ratio (see below)
The basic reproduction ratio LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEnJiM5NjE7RicvJSdmYW1pbHlHUSZBcmlhbEYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRi82I1EhRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y7RjIvJStleGVjdXRhYmxlR0Y3Rjg=, for the SIR model as defined above, can be derived as: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEmJnJobztGJy8lJ2ZhbWlseUdRJkFyaWFsRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GLzYjUSFGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRjstSSNtb0dGJDYuUSJ+RicvJStleGVjdXRhYmxlR0Y3RjgvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZXRkEtRkI2LlEiPUYnRkVGOEZHRklGS0ZNRk9GUUZTL0ZWUSwwLjI3Nzc3NzhlbUYnL0ZZRmhuRkEtSSZtZnJhY0dGJDYoLUYjNigtRi82JVEnJiM5NDY7RidGNUY4LUZCNi1RJyZzZG90O0YnRjhGR0ZJRktGTUZPRlFGU0ZVRlgtRi82JVEnJiM5NjM7RidGNUY4RkUvJTBmb250X3N0eWxlX25hbWVHUSgyRH5NYXRoRidGOC1GIzYpLUkobWZlbmNlZEdGJDYkLUYjNiktRi82JVEnJiM5NTY7RidGNUY4LUZCNi1RIitGJ0Y4RkdGSUZLRk1GT0ZRRlMvRlZRLDAuMjIyMjIyMmVtRicvRllGaXAtRi82JVEnJiM5NDc7RidGNUY4L0Y2USV0cnVlRidGRUZoby9GOVEnaXRhbGljRidGOEZiby1GXnA2JC1GIzYpRmJwRmVwRmVvRl5xRkVGaG9GYHFGOEZecUZFRmhvRmBxLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Zbci8lKWJldmVsbGVkR0Y3RkVGaG9GOA==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
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].<Text-field style="Heading 2" layout="Heading 2"><Font family="Arial">Interactive SEIR model: Infectious Disease Nonlinear Compartment Model 3</Font></Text-field>
Infection rate (\316\262)Exposed (Infected)-to-Infectious rate (\317\203)SEIRmodel:-MakePlotSEIRsol() ;
JSFHSEIRmodel:-MakePlotSEIRsol() ;
What happens when \317\203 = 1.0 as compared to \317\203 = 0.1? 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;JSFHSEIRmodel:-MakePlotSEIRsol() ;Removal rate (\316\263)Life expectancy (1/\316\274)
What happens when \317\203 = 1.0 as compared to \317\203 = 0.1? Why is this a crucial parameter available only in this model?
Model summaryParameter nameSymbolValueSusceptibles, fraction at t=0LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiU0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtSSNtbkdGJDYlUSIwRidGMi9GNlEnbm9ybWFsRidGMkZBRjJGQUYyRkE=JSFHExposed (Infected), fraction at t=0LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiRUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtSSNtbkdGJDYlUSIwRidGMi9GNlEnbm9ybWFsRidGMkZBRjJGQUYyRkE=Infected and infectious, fraction at t=0LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtSSNtbkdGJDYlUSIwRidGMi9GNlEnbm9ybWFsRidGMkZBRjJGQUYyRkE=JSFHRecovered, fraction at t=0LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtSSNtbkdGJDYlUSIwRidGMi9GNlEnbm9ybWFsRidGMkZBRjJGQUYyRkE=JSFHBirth rate=Death 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Life expectancyLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkmbWZyYWNHRiQ2KC1JI21uR0YkNiVRIjFGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYmLUkjbWlHRiQ2JlEnJiM5NTY7RicvJSdpdGFsaWNHRjRGMkY1L0Y/USV0cnVlRidGMi9GNlEnaXRhbGljRicvJS5saW5ldGhpY2tuZXNzR0YxLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRkgvJSliZXZlbGxlZEdGNEYyRjU=Infection rateLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEnJiM5NDY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGMkY0JSFHExposed (Infected)-to-Infectious rateLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEnJiM5NjM7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGMkY0Removal rateLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEnJiM5NDc7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGMkY0JSFHBasic reproduction 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JSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiUtRi82JlEjZXFGJ0YyRjVGOEY1L0Y5USdub3JtYWxGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRjVGQA==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5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JSFH<Text-field style="Heading 2" layout="Heading 2"><Font family="Arial">References</Font></Text-field>Keeling MJ, Rohani P [2008]: Modeling Infectious Diseases in Humans and Animals. Princeton University Press, Princeton and OxfordKermack WO, McKendrick AG [1927]: A contribution to the Mathematical Theory of Epidemics. Proc. Roy. Soc. A 115, 700-711 (Download link)JSFHJSFHJSFH