Electronic Thesis and Dissertation Repository


Doctor of Philosophy


Applied Mathematics


Dr. Xingfu ZOu


The aim of this thesis is to understand the spread, persistence and prevention mechanisms of infectious diseases by mathematical models. Microorganisms that rapidly evolve pose a constant threat to public health. Proper understanding of the transmission machinery of these existing and new pathogens may facilitate devising prevention tools. Prevention tools against transmissions, including vaccines and drugs, are evolving at a similar pace. Efficient implementation of these new tools is a fundamental issue of public health. We primarily focus on this issue and explore some theoretical frameworks.

Pre-exposure prophylaxis (PrEP) is considered one of the promising interventions against HIV infection as experiments on various groups and sites have reported its significant effectiveness. This study evaluates the effectiveness of Tenofovir gel, one of the widely used PrEPs for women, through a mathematical model. Our model has excellent agreement with the experimental data on the use of Tenofovir gel as a PrEP in South African women. Using our model, we estimate both male-to-female and female-to-male transmission rates with and without Tenofovir gel protection. Through these estimates, we demonstrate that the use of Tenofovir gel as a PrEP can significantly reduce the reproduction numbers, new infections, and HIV prevalence in South Africa. Our results further show that the effectiveness of Tenofovir gel largely depends on the level of adherence to the gel and the proportion of women under gel coverage. Even though Tenofovir gel alone may not be able to eradicate the disease, as indicated by our estimates of the reproduction numbers, together with other interventions, such as condom use, it can serve as a strong weapon to fight against HIV epidemics.

Another promising drug-oriented intervention against HIV infection is antiretroviral treatment (ART). We study some crucial aspects of this intervention on the HIV epidemic. ART has the potential to reduce mortality and disease progression among HIV infected individuals. It can reduce the viral load of the infected individual to an undetectable level and help prevent new infections. Whether the treatment should begin early or be delayed is still under debate. This study considers the impact of early versus delayed ART on the HIV epidemic and demonstrates the optimum timing of ART initiation. Our results highlight the long-term consequences of early treatment.

Finally, we investigate the consequences of vaccine implementation strategies for infectious diseases. Vaccines are said to be the intervention with the most potential against many infectious diseases. However, their success relies on proper and strategic management and distribution. In an infectious disease, the degree of infection may vary widely among those individuals. Reports show that individuals belonging to certain groups possess considerably higher risk for infection. Integrating this phenomenon into vaccination strategies, the host is categorized into different groups to measure the outcome of the vaccination. A mathematical model is proposed and analyzed to evaluate this measure. Our results suggest that vaccinating a group with a certain priority may lead to effective elimination of the disease.