| In mathematical epidemiology, the standard
compartmental models assume homogeneous mixing in the host
population, in contrast to the disease spread process over a real
host contact network. One approach to incorporating heterogeneous
mixing is to consider the population to be a network of individuals
whose contacts follow a given probability distribution. In this
thesis we investigate in analogy both homogeneous mixing and contact
network models for infectious diseases that admit latency periods,
such as dengue fever, Ebola, and HIV. We consider the mathematics of
the compartmental model as well as the network model, including the
dynamics of their equations from the beginning of disease outbreak
until the disease dies out. After considering the mathematical
models we perform software simulations of the disease models. We
consider epidemic simulations of the network model for three
different values of R0 and compare the peak infection numbers and
times as well as disease outbreak sizes and durations. We examine
averages of these numbers for one thousand simulation runs for three
values of R0. Finally we summarize results and consider avenues for
further investigation. |