Date of Award

Fall 2014

Degree Type


Degree Name

Doctor of Philosophy (PhD)



First Advisor

Zhilan Feng

Committee Chair

Zhilan Feng

Committee Member 1

Christopher Kribs-Zaleta

Committee Member 2

Aaron Nung Kwan Yip

Committee Member 3

Gregery Buzzard


This thesis includes modeling studies on three structured deterministic models. These models are used to study the disease dynamics of malaria or the joint disease dynamics of HIV and HSV-2. Each of the models includes multiple components containing individuals in various epidemiological classes for the purpose of addressing questions that are of interests to biologists and epidemiologists. Some of the compartments have a continuous age-structure, which is necessary for studying the specific biological questions under investigation.^ In Chapter 2 a chronological-age structured deterministic model for malaria is presented. The model includes the human and mosquito populations with the human population structured by chronological age. The model consists of both PDEs and ODEs. The infected human population is divided into symptomatic infectious, asymptomatic infectious and asymptomatic chronic infected individuals. The original PDE model is reduced to an ODE model with aging. The basic reproduction number R0 is derived for both settings of the model. A novel assumption of the model based on biological evidence is that the infectiousness of chronic infected individuals can be triggered by bites from even susceptible mosquitoes. The model analysis indicates that this assumption contributes greatly to the R0 and therefore needs to be further studied and understood. Numerical simulations for n =2 age groups and a sensitivity/uncertainty analysis show that it is important to both asymptomatic infectious individuals and asymptomatic chronic infections. Age-targeted control strategies are also discussed.^ In Chapter 3 a deterministic malaria model is presented to study the effects of a pre-erythrocytic vaccine on malaria dynamics. The model includes two vaccinated classes, the first for initial vaccination dose(s) and the second for a booster dose. Vaccinated individuals in both compartments are structured by vaccine-age. A vaccine-age dependent transition between vaccinated classes makes it possible to model a minimum vaccine-age required for receiving the booster vaccination. The control reproduction number R is derived and shown to determine the local stability of the disease free equilibrium. Global stability of the disease free equilibrium is shown analytically under certain assumptions and conditions for the existence of endemic equilibria are identified. Numerical results suggest that the incorporation of two vaccination classes, as opposed to only one, allows for a greater accuracy in predicting threshold vaccination coverages for disease eradication. The model also exhibits backward bifurcation, indicating thatR=1 is no longer the threshold value for disease eradication. The effect of waning vaccine efficacy (vaccine-age dependent) on disease prevalence is also investigated. ^ Chapter 4 presents a deterministic model for the joint dynamics of HIV and HSV-2 to study the effect that the presence of HSV-2 may have on the prevalence of HIV. An infection-age is used to incorporate the epidemiological characteristic of HSV-2 that infected individuals change between the acute and the latent stages, and treatment may affect the lengths of these stages. The model is also structured by gender and includes one male and two female populations with different activity levels. The basic reproduction number for each disease, as well as the invasion reproduction numbers are derived. Due to the model complexity, the derivation of these reproduction numbers and their biological interpretations are very challenging, which is one of the novel aspects of this study. Numerical simulations are performed to confirm and extend the analytical results. A sensitivity analysis is also conducted. Model results demonstrate that strategies for reducing co-infections with HIV and HSV-2, particularly treating the high-risk group of females may have an important impact on the HIV disease dynamics.