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ODEs in Mathematical Medicine: New Virus Dynamics in the Presence of Multiple Infection; Evolution of Genetic Instability in Heterogeneous Tumors

  • Author(s): Asatryan, Ani Davitovna
  • Advisor(s): Komarova, Natalia L
  • et al.

In this dissertation two independent studies are presented in the field of ordinary differential equations. In the first part we introduce a novel model of viral dynamics to describe the phenomenon of multiple infection. An important parameter in determining the properties of the model is the viral output of multiply infected cells compared to that of singly infected cells. If multiply infected cells produce more virus during their life-span than singly infected cells, then the properties of the viral dynamics can change fundamentally. The first part of this study presents a detailed mathematical analysis of this scenario.

In the second part we develop a class of mathematical models to study the evolutionary competition dynamics among different sub-populations in a heterogeneous tumor. We observe that despite the complexity of this system there are only a small number of scenarios expected in the context of the evolution of instability. Here we discuss these scenarios and their dependence on the subtle interplay among mutation rates and the death toll associated with instability. We also present possible patterns of instability for cancer lineages corresponding to different stages of progression and determine whether instability plays a causal role in tumor evolution.

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