differential equations

where is a positive proportionality factor, and y0 is the initial proportion of infectious individuals. a. Find the equilibrium points for the differential equation (22) and determine whether each is asymptotically stable, semistable, or unstable. b. Solve the initial value problem 22 and verify that the conclusions you reached in part a are correct. Show that y(t) 1 as t, which means that ultimately the disease spreads through the entire population. where is a positive proportionality factor, and y0 is the initial proportion of infectious individuals. a. Find the equilibrium points for the differential equation (22) and determine whether each is asymptotically stable, semistable, or unstable. b. Solve the initial value problem 22 and verify that the conclusions you reached in part a are correct. Show that y(t) 1 as t, which means that ultimately the disease spreads through the entire population