A new virus emerges in a population. Each day, 10% of the susceptible population becomes

Chapter 12, Problem 12.5.10

(choose chapter or problem)

A new virus emerges in a population. Each day, 10% of the susceptible population becomes infected, and 50% of the infected population recovers. Additionally, 2% of the recovered population becomes reinfected. Let p = (s, i, r) be a population vector where s is the number of susceptible (never-infected) people, i is the number of infected people, and r is the number of recovered people, all numbers in millions. Assume that initially p0 = (2, 0, 0). (a) Find a matrix T such that p new = Tp old where p old is the starting population and p new is the population a day later. (b) Find p1 , p2 , and p3 , the populations on days 1, 2, and 3, respectively. 10. A ce depends only on sold. (a) Suppose P new = TP old = 0.3 0.6 0.5 0.70 0 0 0.4 0 P old. Describe in words what this tells you about the life cycle of this insect. Be specific. (b) Let P0 = (2000, 0, 0) be the initial population vector in year t = 0. Evaluate P1 , P2 , and P3 . 11. Let