Modeling, analysis, and simulation of complex disease dynamics for HIV, Ebola, and Zika virus

Abstract

The contributions made by mathematical approaches to biological problems has become widely recognized in recent decades. The focus of this thesis is to develop and analyze novel mathematical models for various aspects of three infectious diseases: Human Immunodeficiency Virus (HIV), Ebola virus disease (EVD) and Zika virus. HIV is examined at the in-host level by two models capturing two stages of the disease process within the blood. The first HIV model considered here incorporates the effects of latent infection and mutation of the virus. This research is meant to provide applicable information when considering various vaccine developments and combination strategies to maintain viral suppression. The second HIV model in this dissertation examines early stage viral development and the contribution of the homeostatic proliferation of CD4+ T cells on the dynamics of the disease process; in particular the dependence of long term outcomes on the initial viral load and healthy T cell count. Both EVD and Zika are analyzed at the epidemiological level with compartmental model structures. A branching SEIR Ebola model is embedded into a stochastic process by means of a novel multinomial distribution derivation. This model is used to determine the most prominent forces of infection causing the 2014 Ebola outbreak in West Africa based on data as recorded by the World Health Organization. Finally, the spread of Zika within Central and South American countries is modeled by way of a modified (SEIR)/SEI vector compartmental structure to estimate basic reproductive numbers, total outbreak size, and reporting rates for Colombia, El Salvador and Suriname. This study highlights the need for research and data collection that will better constrain parameter ranges.