Epidemic models are used as a tool to analyze the behaviors of biological diseases and how they spread. In the SI epidemic model, where S represents the group of susceptibles and I represents the group of infectives, the numerical outputs can be nonintegers, which creates obstacles in applying these results to our biological reality. Here, we discretize the model output values by applying various combinations of integerizing (Round, Ceiling, Floor). These discretized values allow the results of the SI model to be applied to reality in terms of whole person outputs. Nine potential discretized SI models are formed with the combinations of integerizing. We eliminate several of these potential models because they do not meet the fundamental property of the SI model -- fixed population size. We compare the properties of the three models that meet the fundamental property with the properties of the original (nondiscretized) SI model. Several unexpected results appear, such as a basic reproduction number, R_0, for two of the three discretized models; the original SI model has no such R0 value.
Prof. Anna Mummert, Department of Mathematics, Marshall University
Sutton, Kacie M.
"Discretizing the SI Epidemic Model,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 15
, Article 12.
Available at: http://scholar.rose-hulman.edu/rhumj/vol15/iss1/12