Simulate the population dynamics involving the growth and decay of an infectious, but easily curable disease. The disease occurs within a single population, and recovery from the disease results in immunity. The population consists of the following three groups: (1) those who are well, but susceptible; (2) those who are sick; and (3) those who are cured and therefore immune. Although the system’s state actually changes discretely, we will assume that we can approximate the system with continuous-change variables describing the size of each group. kel01315_ch11_479-518.indd 516 05/12/13 3:19 PM Continuous and Combined Discrete/Continuous Models 517 We will use the state variables named Well, Sick, and Cured to denote each group’s current size. Initially, the Well population size is 1,000, the Sick population is 10, and the Cured is 0. The following system of differential equations governs the infection rate, where d/dt indicates the rate of change of the population size. d/dt (Well) 5 20.0005 3 Well 3 Sick d/dt (Sick) 5 0.0005 3 Well 3 Sick 2 0.07 3 Sick d/dt (Cured) 5 0.07 3 Sick Assuming that these formulas are based on days, how long will it take until the size of the Well group decreases to 2% of its original size? Include a plot of the three populations.