PROBLEM 16E

(a) In Problem 15, explain why it is sufficient to analyze only

(b) Suppose k1 = 0.2, k2 = 0.7, and n = 10. Choose various values of i(0) = i0, 0 < i0 < 10. Use a numerical solver to determine what the model predicts about the epidemic in the two cases s0 > k2/k1 and s0 k2/k1. In the case of an epidemic, estimate the number of people who are eventually infected.

Reference: Problem 15

SIR Model Acommunicable disease is spread throughout a small community, with a fixed population of n people, by contact between infected individuals and people who are susceptible to the disease. Suppose that everyone is initially susceptible to the disease and that no one leaves the community while the epidemic is spreading. At time t, let s(t), i(t), and r(t) denote, in turn, the number of people in the community (measured in hundreds) who are susceptible to the disease but not yet infected with it, the number of people who are infected with the disease, and the number of people who have recovered from the disease. Explain why the system of differential equations

where k1 (called the infection rate) and k2 (called the removal rate) are positive constants, is a reasonable mathematical model, commonly called a SIR model, for the spread of the epidemic throughout the community. Give plausible initial conditions associated with this system of equations.

Stress and Disease Promoting Health ❖ Aerobic exercise ➢ Sustained exercise that increases heart and lung fitness ➢ May also alleviate depression and anxiety ❖ Biofeedback ➢ You can set up electronic sensor that detects breathing/heart rate and you can consciously practice slowing down heart rate ❖ Biofeedbacks lowtech cousin:...