ME/ECE859-Spring 2008 Homework 2, Due date: 1/30/08 WedThe spread of infective diseases can be modeled as a nonlinear system.We introduce herethe SIRS model. The population consists of three disjoint groups. The population of susceptibleindividuals is denoted byS, the infected population byI, and the recovered population byR. Weassume that the total population, which is denoted byτis constant, so thatddt(τ=S+I+R) = 0.We assume that the rate of transmission of the disease (denoted byβ) is proportional to thenumber of encounters between susceptible and infected individuals. Also assume that the return ofrecovered individuals to the classSoccurs at a rate (denoted byμ) proportional to the populationof recovered individuals (like malaria and tuberculosis).Finally assume that the rate at whichinfected individuals recovers (denoted byν) is proportional to the number of infected. Hence theSIRS model is given bydSdt=-βSI+μRdIdt=βSI-νIdRdt=νI-μR,whereβ, μ, νandτare positive real numbers. Sinceτ
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