Suppose we have a population of size n where individuals are either diseased or susceptible to disease. Susceptible individuals develop have a constant hazard o of developing disease, and diseased individuals have a constant hazard S of recovering from disease. Once recovered, they go back to being susceptible. Let p be the point prevalence of disease at time t, and let (t, t + di] be a short time interval. (a) Among people who are susceptible at time t, what is the cumulative incidence of disease in the time interval (t,t + di]? What is the expected number of people who develop disease in this time interval? (b) What is the mean duration of disease? Among people who have disease at time t, what is the cumulative incidence of recovery in the time interval (t, t + dt]? What is the expected number of people who recover in this time interval? (c) At equilibrium, we should have approximately the same number of disease onsets and recoveries in each time interval (t, #+di]. Let P be the prevalence of disease at equilibrium. Show that, at equilibrium, the prevalence odds P/(1 - P) equals a/B. (d) Show that, when P is small, P= a/B