Date of Award

8-2016

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics

First Advisor

Zhilan J. Feng

Committee Chair

Zhilan J. Feng

Committee Member 1

Gregery T. Buzzard

Committee Member 2

John W. Glasser

Committee Member 3

Andrew N. Hill

Committee Member 4

Yip K. Nung

Abstract

This thesis focuses on applying mathematical models to studies on the transmission dynamics and control interventions of infectious diseases such as Ebola virus disease and vaccine preventable diseases.

Many models in studies of Ebola transmission are based on the model by Legrand et al. (2007). However, there are potential issues with the Legrand model. First, the model was originally formulated in a complex form, leading to confusion and hindering its uses in practice. To overcome the difficulty, the Legrand model is reformulated in a much simpler but equivalent form in this thesis. The reformulated model also provides an intuitive understanding of its parameterization. Second, the underlying assumptions of the Legrand model are not mathematically clear for researchers, which might lead to inadvertent misuse of the model. The assumptions are clearly identified through comparison with three models developed with clear assumptions in this thesis, one of which simplifies to the Legrand model. This three models are also built with more realistic sojourns of epidemiological processes. The comparison among these models also demonstrates the importance of the underlying assumptions as they may provide different implications on control strategies.

In addition, a concern about current Ebola models is that many of them consider only infections with typical symptoms, but Ebola presents clinically in a more complicated way. To account crudely for the wide spectrum of clinical symptoms that characterizes Ebola infection, a model is developed including asymptomatic, mild and severe infections. Comparing to the model with only typical symptoms, it shows that modeling the spectrum is important as it could affect estimation of the reproduction number and effectiveness of interventions. Possible effective control strategies are also evaluated. We show that the spectrum of Ebola infection is important in modeling as it has implications for policy-making.

In many parts of the world, people seasonally migrate between rural and urban/peri-urban patches for economic opportunities. Migration meanwhile changes the immunity levels of patches and might increase the chance of recurrent outbreaks of vaccine preventable diseases. A three-patch meta-population model is developed that incorporates spatially explicit migration of individuals. The model is used to evaluate vaccination strategies to mitigate outbreaks. It suggests that rural-urban migration is an important factor in designing public health policies to mitigate vaccine-preventable diseases.

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