We consider an extension of the standard SIR model discussed in the lectures, in which the population is divided into 4

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We Consider An Extension Of The Standard Sir Model Discussed In The Lectures In Which The Population Is Divided Into 4 1 (201.69 KiB) Viewed 33 times

We consider an extension of the standard SIR model discussed in the lectures, in which the population is divided into 4 distinct groups: susceptible individuals S(t), exposed individuals Eſt) who have been infected but are not contagious yet, infected and infectious individuals I(t), and recovered (temporary immune) individuals R(t), which are all functions of time t (in days). The new model is based on the following assumptions. 1. The total population is constant, i.e. s(t) + E(t) + I(t) + R(t) = N. 2. Susceptible individuals are getting infected at a rate proportional to the number of infectious individuals (infection rate of B = 0.01 per infectious individuals per day). Susceptible individuals who are infected become exposed and are not infectious yet. 3. Exposed individuals become infectious at a constant rate of 8 = 0.2 per day. 4. Infectious individuals recover at a constant rate of y = 0.1 per day. 5. Recovered individuals lose their immunity after a while and so become susceptible again at a constan rate of a = 0.01 per day. Write down the system of differential equations consistent with the assumptions above. For the rates a, b, y and 8, give their corresponding numerical values in the differential equations below. ds II dt dE = dt dl dt dR = dt