Modeling the spread of disease through a population

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