Suppose that a community contains 15,000 people who are susceptible to a contagious disease. If N(t)...

Suppose that a community contains 15,000 people who are susceptible to a contagious disease. If N(t) represents the number of people who have become infected in thousands, where t is time in days, and N′(t) is proportional to the product of the numbers of those who have caught the disease and of those who have not. The following logistic model can be used to model the spread of the disease.

dN/dt= 1N(15−N) dt 100

(a) Sketch the phase line (portrait) and classify all of the critical (equilibrium) points. Use arrows to indicated the flow on the phase line (away or towards a critical point).

(b) Next to your phase line, sketch a typical solution curve for the differential equation in each of the regions of the tN-plane determined 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.

Expert Solution

Colby Messinger answered 1 year ago

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