2. (SIR Model) The spread of an infectious disease beginning with 1 individual out of 10000 is modeled by the following SIR models: ds CP51 N dt di CP.si - y1 N dt dR =yl dt where c = 20, p = 0.025, and y = 1/4. (a) Assuming that R(0) = 0 initially, calculate a bound on the maximum number of individuals who will catch the disease. (b) Assume that a vaccination program means that half of the population starts out immune to the disease, i.e., R(O) = 5000. Assume also that there are initially 50 infected individuals (i.e. I(0) = 50). Recalculate the maximum bound on the number of individuals who will eventually catch the disease. For question 2, beta is still cp but to estimate the number of infected you should use Imax = N -S(O)e^(-cp/gamma) For part b, you will need to modify the above formula since only half can get infected, You can calculate S(infinity) from the dS/dR equation using R(O)=N/2 to compute the constant of integration. 2. (SIR Model) The spread of an infectious disease beginning with 1 individual out of 10000 is modeled by the following SIR models: ds CP51 N dt di CP.si - y1 N dt dR =yl dt where c = 20, p = 0.025, and y = 1/4. (a) Assuming that R(0) = 0 initially, calculate a bound on the maximum number of individuals who will catch the disease. (b) Assume that a vaccination program means that half of the population starts out immune to the disease, i.e., R(O) = 5000. Assume also that there are initially 50 infected individuals (i.e. I(0) = 50). Recalculate the maximum bound on the number of individuals who will eventually catch the disease. For question 2, beta is still cp but to estimate the number of infected you should use Imax = N -S(O)e^(-cp/gamma) For part b, you will need to modify the above formula since only half can get infected, You can calculate S(infinity) from the dS/dR equation using R(O)=N/2 to compute the constant of integration