13. (2+4+2+4+3=15 points, over two pages) A disease propagates through an isolated community. The population consists of x susceptible individuals and y infected individuals. There is a constant immigration into the community, and at any time, a certain percentage of susceptible individuals who are not infected leave the community. Infected individuals some- times die, and sometimes live but remain infected. A system of nonlinear differential equations describing the dynamics of this disease is given by dx dt = 20 - 5xy - 5x = f(x, y) dy dt = 5xy - 10y = 9(x, y). (a) (2 points) Calculate the nullclines and equilibria of this system of differential equations. Simplify. (b) (4 points) Sketch the nullclines in the phase plane, below. Draw the direction arrows along each pullcline as well as in each of the regions of the first quadrant defined by the nullclines. Circle the equilibria (use bullets!). Label the axes. 15 25 35