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Refer to the simple model of epidemics in Subsection 8.3.1. Divide (8.75) by (8.74) to show that when I > 0, dI/dS = a/b 1/S - 1 Also, show that when R(0) = 0, I(0) = I0, and S(0) = S0, the solution of (8.84) satisfies I(t) = N-S(t) + a/b ln S(t)/S0 where I(t) denotes the number of infectives, N the total number of individuals in the population, and S(t) the number of susceptibles at time t. dN/dt = N1 - aN - r(N)X + mX dX/dt = r(N)X - (m + c)X

Show transcribed image text Refer to the simple model of epidemics in Subsection 8.3.1. Divide (8.75) by (8.74) to show that when I > 0, dI/dS = a/b 1/S - 1 Also, show that when R(0) = 0, I(0) = I0, and S(0) = S0, the solution of (8.84) satisfies I(t) = N-S(t) + a/b ln S(t)/S0 where I(t) denotes the number of infectives, N the total number of individuals in the population, and S(t) the number of susceptibles at time t. dN/dt = N1 - aN - r(N)X + mX dX/dt = r(N)X - (m + c)X