Consider the application of the PSSH to epidemiology. We shall treat each of the following...

Consider the application of the PSSH to epidemiology. We shall treat each of the following steps as elementary in that the rate will be proportional to the number of people in a particular state of health. A healthy person, H, can become all, I, spontaneously, such as by contracting smallpox spores:

or he may become ill through contact with another ill person:

The ill person may become healthy:

or he may expire:

The reaction given in Equation (P7-8.4) is normally considered completely irreversible, although the reverse reaction has been reported to occur.

(a) Derive an equation for the death rate.

(b) At what concentration of healthy people does the death rate become critical? [Ans.: When [H] = (k3 + k4)/k2.]

(c) Comment on the validity of the PSSH under the conditions of part

(d) If k1 = 10−8 h−l, k2 = 10−16 (people-h)−1, K3= 5 X 10−10, k4 = 10−11 h, and Ho = 109 people, use Polymath to plot H, I, and D versus time. Vary k¡ and describe what you find. Check with your local disease control center or search the WWW to modify the model and/or substitute appropriate values of k¡. Extend the model taking into account what you learn from other sources (e.g., WWW).

(e) List ways you can work this problem incorrectly.

(f) How could you make this problem more difficult?