Suppose that a given population can be divided into two parts, those who have a given disease and can infect others, and those who do not have it but susceptible. Assume that y the proportion of infectious individuals then the rate of spread dy/dt is proportional to the number of contacts and can be described as
Where y > 0 is a function of t, is the initial proportion of infectious individuals.
- Use MAPLE and sketch a direction field for your differential equation and include a sufficient number of solution curves and include the graph into your answer sheet.
- Find all the equilibrium solutions and determine whether they are asymptotically stable or unstable.
- Solve the above initial value problem and verify that the conclusions you reached in part(ii) are correct.