There has been increased interest recently for mathematical models of the spread of contagious disease through a population. The purpose of this project is to explore one class of models along with some implications for health-care policy.
One mathematical model for the spread of an infectious disease divides the population into Susceptible, Infective, and Removed classes. A susceptible individual can catch the disease by contact with an infected individual. An infected individual moves on to the removed class by being isolated from the population, recovering (and developing immunity) or dying. Some of the recovered class may eventually loose immunity and return to the susceptible class. Here is a model to start with:
You may use your favorite software (Matlab or Maple or...) to investigate the system and obtain solution curves.
Remark: in some literature on this subject, the quantity is called the intrinsic reproductive rate of the disease. For a recent smallpox epidemic in developing countries, was estimated to be approximately 4. For a measles outbreak in the U.S. in the early part of this century, .
Final Version Due: Thursday, March 6
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