Project 6 returns to the modeling of disease epidemics that was considered in Project 5. This time, however, the project uses a "large scale" model. Instead of looking closely at individuals, the model monitors the health of a very large population. Now there are just a few statistical quantities of interest: S, I, and R, representing the percentages of the populuation that are susceptible, infected, or recovered.
If the population is large enough, and we are interested in the long term progression of the disease, we can treat the statistical quantities as functions of time t, and we write them as S(t), I(t), and R(t). If we make some simple assumptions about the disease, we can approximate the changes in these quantities using a set of three differential equations.
By creating a large scale model, we are able to try to simulate actual epidemics. The differential equations include parameters that try to describe the degree to which the disease is transmissible and the length of time it takes to recover. The model now allows us to experiment with the effect of varying the parameters. Will the disease spike and then disappear? Will everyone get the disease?
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