Modeling the spread of disease through a population
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As disease spreads through a population, scientists want to know who gets sick, how best to prevent a large outbreak, and if an epidemic may occur. For many years, mathematicians used models to approximate answers to these questions; however, these older models used simplifying assumptions about the host population that drastically reduced the accuracy of the model’s predictions. Within the last ten years, however, graph theory was introduced to computational epidemiology so that we now have more realistic models of the contact patterns that facilitate the spread of disease. This thesis used these models in conjunction with probability generating functions to explore the effects of individuals changing contacts during the course of an epidemic on two different degree distributions, the Poisson and the power-law. We found that at all rates of swapping contacts, the total epidemic size for the Poisson distribution is larger than that of the power-law, but that the time to total epidemic size is lower for power-law than for Poisson.