Mathematical modeling of infectious disease

The battleground of infectious disease enlists two chief forces: the defending immune system, and the invading pathogen. The immune system consists of a diverse population of leukocytes that recognize foreign material and defend against pathogens. An outstanding feature of this defense is immunological memory. Immunological memory can develop after infection or vaccination, and provides increased protection to secondary challenge. The cells contributing to memory can be identified phenotypically by protein markers, or kinetically as antigen specific cells that survive population contraction after virus clearance. However, the mechanisms that regulate memory cell development remain unclear.The first half of this thesis explores the defending immune system using mathematical models of lymphocyte differentiation, expansion, and contraction to memory. These models are fitted to a broad range of experimental data and provide a number of insights into T cell and NK cell behavior. Firstly, the results show that a mechanism of division-linked differentiation, where the expression of the memory marker CD62L can randomly down-regulate upon division, explains differences in phenotype observed in adoptive transfer, endogenous and polyclonal CD8 T cell responses. Secondly, the results suggest that the increased protection that experienced NK cells provide is likely to be short-lived. These results may help future vaccine designs to target appropriate lymphocyte subsets.For the second half of this thesis, the focus shifts from the defending immune system, to the invading pathogen. Here I focus on the life cycle of the HIV virus. HIV evades immune pressure by maintaining high levels of diversity throughout infection. This diversity is principally generated by mutation and recombination during reverse transcription. However, current estimates of HIV-1 recombination rates do not compensate for undetectable recombination occurring over genomically identical regions. The measurements of recombination rate are also derived from genetically divergent HIV sequences or within foreign gene inserts. This thesis develops statistical tools for calculating recombination rates (considering undetectable recombination) and applies them to a novel experimental method, to accurately calculate the recombination rate between homologous and 'natural' HIV strands.The findings on the defending immune system and invading pathogen demonstrate the power of mathematical analysis when complemented with experimental data