UC Irvine

The following thesis explores the within-host population dynamics of viruses and their target cells using mathematical and computational models. Chapter 1 investigates the dynamics that arise when two independently regulated HIV-specific t helper cell populations grow by clonal expansion in response to antigenic stimulation by HIV. Despite no direct competition for antigenic stimulation, we find that it is still possible for the stronger clone to drive the weaker clone to extinction through the process of apparent competition. In addition, we find that under certain conditions a weaker clonal population can be facilitated by the presence of a stronger one, causing the weaker clone to become established where it would have failed to persist in isolation. Chapter 2 explores the regulation of tissue architecture in a model of stem cells and differentiated cells. We investigate two types of feedback regulation, and discuss how these regulatory controls influence the ability to maintain tissue homeostasis during viral infections. We find that when feedback factors are produced by stem cells, viral infection leads to a significant reduction in the number of differentiated cells (tissue pathology), while the number of stem cells is not affected at equilibrium. In contrast, if the feedback factors are produced by differentiated cells, a viral infection never reduces the number of tissue cells at equilibrium because the feedback mechanism compensates for virus-induced cell death. However, the number of stem cells becomes elevated, which could increase the chance of these stem cells to accumulate mutations that drive cancer. In Chapter 3, we investigate viral infection in an agent-based model, allowing us to simulate in-host microenvironments that have some spatial structure, such as the lymph nodes. The model explores the consequences of multiple infection and an increased burst size on the dynamics of early viral spread through host cells. We find that the model predicts larger proportions of multiply infected cells at low viral loads in environments where mobility is limited. In addition, when an increased burst size in multiply infected cells is included in the model, both accelerated viral spread and a decreased probability of infection extinction are observed.