Suppose that a community contains 15,000 people who aresusceptible to a contagious disease. If N(t) represents the numberof people who have become infected in thousands, where t is time indays, and N?(t) is proportional to the product of the numbers ofthose who have caught the disease and of those who have not. Thefollowing logistic model can be used to model the spread of thedisease.
dN/dt= 1N(15?N) dt 100
(a) Sketch the phase line (portrait) and classify all of thecritical (equilibrium) points. Use arrows to indicated the flow onthe phase line (away or towards a critical point).
(b) Next to your phase line, sketch a typical solution curve forthe differential equation in each of the regions of the tN-planedetermined by the graph(s) of the equilibrium solution(s).
(c) Solve the initial-value problem dN/dt = (1/100) N (15 ? N ), N (0) = 10 with Separation of Variables. You may leave
your solution in implicit form.
