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By James Callahan, Kenneth Hoffman, David Cox, Donal O’Shea ,Harriet Pollatsek, Lester Senechal

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We have already travelled one way by constructing a mathematical object that reflects some aspects of the epidemic. This is model-building. Presently we will travel the other way. First we need to Copyright 1994, 2008 Five Colleges, Inc. 1. THE SPREAD OF DISEASE 11 get mathematical answers to mathematical questions; then we will see what those answers tell us about the epidemic. This is interpretation of the model. Before we begin the interpretation, we must do some mathematics. Analyzing the Model Now that we have a model we shall analyze it as a mathematical object.

If there were fewer than 7143 susceptibles in the population at the outset, then the number of infected would only decline with each passing day. The infection would simply never catch hold. The clear implication is that the noticeable surge in the number of cases that we associate with an “epidemic” disease is due to the presence of a large susceptible population. If the susceptible population lies below a certain threshold value, a surge just isn’t possible. This is a valuable insight—and we got it with little effort.

Continue to assume we start with S = 45400. e) Suppose the initial susceptible population is 45,400. What is the largest value that the transmission coefficient can have and still guarantee that I never goes up? What level of quarantine does this represent? That is, do you have to reduce the chance that a susceptible will fall ill to one-third of what it was with no quarantine at all, to one-fourth, or what? Other Diseases 20. 08 I. Note: the initial values S = 45400, etc. that we used in the text do not apply here.

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