Question: Direction field using Maple

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

=y(-y), y(0)=y₀

Where y > 0 is a function of t,  is the initial proportion of infectious individuals.

1. 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.

(3 marks)

2. Find all the equilibrium solutions and determine whether they are asymptotically stable or unstable.

(4 marks)

3. Solve the above initial value problem and verify that the conclusions you reached in part(ii) are correct.

(5 marks)