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hw2 - ME/ECE859-Spring 2008 Homework 2 Due date Wed The...

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ME/ECE859-Spring 2008 Homework 2, Due date: 1/30/08 Wed The spread of infective diseases can be modeled as a nonlinear system. We introduce here the SIRS model. The population consists of three disjoint groups. The population of susceptible individuals is denoted by S , the infected population by I , and the recovered population by R . We assume that the total population, which is denoted by τ is constant, so that d dt ( τ = S + I + R ) = 0. We assume that the rate of transmission of the disease (denoted by β ) is proportional to the number of encounters between susceptible and infected individuals. Also assume that the return of recovered individuals to the class S occurs at a rate (denoted by μ ) proportional to the population of recovered individuals (like malaria and tuberculosis). Finally assume that the rate at which infected individuals recovers (denoted by ν ) is proportional to the number of infected. Hence the SIRS model is given by dS dt = - βSI + μR dI dt = βSI - νI dR dt = νI - μR, where β, μ, ν and τ are positive real numbers. Since τ
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