From the Logistic Model to the SIR Model for an Epidemic: Example from the 2003 SARS Epidemic in Hong Kong
In this article we use spreadsheet technology to construct a distribution function (logistic) for the 2003 Hong Kong severe acute respiratory syndrome (SARS) epidemic. From the distribution function, we deduce an equivalent density function which predicts the daily reported cases for the epidemic. This density function is used as the infection function in the SIR modeling for the epidemic. There was no significant difference (p-value= 0.192) between the mean number of the actual daily reported cases of the disease, and the mean number of predicted daily cases of the disease using the density function. We calculate an infection rate for the SIR model and estimate the basic reproductive number (R_o=2.88) for the epidemic; this value is within the range 2 - 4 reported by other studies on the Hong Kong SARS. The approach used, provides a modeling example using spreadsheet technology that is available to teachers and the high school students they teach.
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