A simple model of the spread of an infection in a population is -kIS kIS, where S(t) is the number of susceptible people, I(t) is the number of infected people and k is a positive constant. We shall be studying such sets of equation later in the course, but for d [S+I] = 0 i.e. the population size is constant so S+I = N say. Substitute dt now note that I = N – S in order to obtain a single equation for S(t), dS :-kS(N – S). dt Determine the stability of the fixed points of this equation, and draw its phase diagram. Deduce that eventually all the population becomes infected.

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