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Mathematical and Computational Models of Virus Dynamics


Mathematical and computational models can provide unique insights into the dynamics of host-pathogen interactions in vivo. This dissertation explores these models in the context of multiple infection of cells and oncolytic virus therapy. In chapter one, we investigate the modeling of multiple infection using systems of ordinary differential equations, and demonstrate that the artificial truncation of the infection cascade required of numerical simulations can affect the distribution of multiply infection cells. As a result, models of multiple infection described by systems of differential equations require careful selection of parameter values and an appropriate cascade length to insure incorrect results are not observed. Chapter two explores this idea further in the context of two competing virus strains. Here, we find that cascade length can affect the equilibrium level of populations in numerical simulations. More specifically, competitive exclusion can be observed for shorter cascade lengths, whereas coexistence can be observed for longer cascade lengths. We also explore these models in a parameter regime in which cascade length does not affect the numerical simulations, and find that multiple infection can promote coexistence if there is a degree of intracellular niche separation. We further find that multiple infection has a reduced ability to promote coexistence if virus spread is spatially restricted compared to a well-mixed system. Finally, chapter three presents an agent-based model of oncolytic virus therapy for the eradication of drug resistant cancer cells. Our results demonstrate that even if it is not possible to eradicate cancer with oncolytic viruses, it may be possible to eradicate the subpopulation of drug resistant cancer cells through apparent competition. Furthermore, we find that an increase in the infection efficiency of the virus can lead to higher levels of suppression of drug resistant cancer cells. This can increase the success rate of subsequent drug therapies in eradicating the cancer.

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