Let x(t)≥0 denote the size of the healthy population and y(t)≥0 denote the size of the sick population. Then the model is given by x
˙
=−kxy, y
˙
​
=kxy−ly where k,l>0. Find and classify all fixed points. Sketch the nullclines and the vector field. Plot the phase portrait. Let (x 0
​
,y 0
​
) be the initial condition. An epidemic is snid to occcur if y(t) increases initially. Under what conditions does an epidemic occur?