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# notes07[1] - Math 19. Lecture 7 Phase Plane Analysis T....

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Math 19. Lecture 7 Phase Plane Analysis T. Judson Fall 2006 1 SIR Models Systems of diﬀerential equations are very useful in epidemiology. We can use diﬀerential equations to model how a disease will spread through a popula- tion. Let us assume that we have a closed population of size N and that each individual in the population falls into one of the following categories: S ( t ) = Susceptible individuals I ( t ) = Infected individuals R ( t ) = Removed individuals Susceptible individuals who do not yet have the disease and can catch the disease from infected individuals. Individuals enter the removed population by either recovering from the disease or dying. If an infected individual recovers, then the individual is immune to the disease. Since the population is closed, we know that S ( t ) + I ( t ) + R ( t ) = N. We can model how the disease acts with the following system of equations, dS dt = - αSI dI dt = αSI - βI. 1

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2 An Epidemic Model Consider the model of a viral epidemic that moves through an isolated pop- ulation. We make the following assumptions. (a) Individuals are infected at a rate proportional to the product of the
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## This note was uploaded on 09/22/2010 for the course MAE MAE294B taught by Professor Mae294b during the Winter '09 term at UCSD.

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notes07[1] - Math 19. Lecture 7 Phase Plane Analysis T....

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