| The study of the population dynamics of disease ranges from the scale of individual cells interacting with virus particles to the structure of the host interaction network. This thesis represents a broad survey of the mathematics of disease across these scales. I have used differential equations to examine the role of competition among viral strains on the progression of HIV infected persons to AIDS, and the factors that lead to the persistence of viral replication in HIV patients undergoing potent drug therapies. At the epidemic level, I have used difference equations to understand the effect of pathogen mutation and host immunity on disease persistence. I have used generating function methods and concepts from graph theory to probe the kinds of host interactions, in particular the distribution of contact rates, which lead to successful vaccination programs. Lastly, I have explored a model of network growth to examine the assumptions made in previous work. |
