number 41 and 43 for section 8.3

8.3.5 To model the spread of a disease in a population of size N we derived a differential equation model: di kb = (kb - c)l - N (8.70) where I(t) is the number of infected individuals at time t, and k, b, and c are all positive coefficients. Assuming that I (t) is modeled by Equation (8.70), in Prob- lems 41-44, you should locate the equilibria of the model, and find which of these equilibria are stable. Draw a vector field plot for each problem. 41. k = 1, b = 1, c = 0.5, N = 50. 42. k = 1, b = 1, c = 0.5, N = 200. 43. k = 2, b = 2, c = 1. N = 100