A communicable disease is spread throughout a small community, with a fixed popu

Question

A communicable disease is spread throughout a small community, with a fixed population of n people, by contact between infected persons and persons who are susceptible to the disease. Suppose initially that everyone is susceptible to the disease and that no one leaves the community while the epidemic is spreading. At time t, let s(t), I(t), r(t) denote, respectively, 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 ahve recovered from the disease. Explain why the system of differential equations ds/dt = -a si di/dt = -bi+ a si dr/dt = bi where a (called the infection rate), and b (called the removal rate) are positive constants, is a reasonable mathematical model for the spread of the epidemic throughout the community.

Explanation / Answer

It's a good mathematical model because in ds/dt if the time increases, people yet don't infected will decrease their probability to be infected in a constant form. In dr/dt, the amount of people who have recovered from the disease will change with the removal rate and the number of people infected and in di/dt is the fusion of the previous, it's an intermediate point.

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