Studies of dynamics of infectious diseases using mathematical models

Yiding Yang, Purdue University

Abstract

This thesis centers on the study of transmission dynamics of infectious diseases using mathematical models. It includes two main topics. The first one concerns the evolutionary dynamics of the human-schistosome-snail system. The second topic is on the evaluation of disease control strategies for directly transmitted infections such as influenza and SARS. The models attempt to answer specific biological questions that are of interest to biologists and policy-makers for public health. The model for human-schistosomesnail interactions is used to study questions including the impact of drug-treatment of human hosts and drug-resistance of parasites within human hosts as well as the role of parasite virulence on the the evolutionary dynamics of intermediate snail hosts. The models for directly transmitted diseases are employed to generate helpful information that can assist policy-makers in disease control and intervention. More specifically, for the human-schistosome-snail system, our model includes two snail host types and a single parasite strain. An age-structure of human hosts is also considered to reflect the age-dependent transmission rate and age-targeted drugtreatment rate. We consider various biological factors that may affect the evolutionary dynamics of host-parasite interactions. By assuming various trade-offs between parasite drug-resistance and the associated fitness cost and between snail resistance to the parasite and the associated cost in reproduction, we investigate the roles of drug-treatment rate, drug-resistance level, and parasite virulence on the evolutionary outcomes of the host-parasite system. Many existing epidemiological models have assumed that disease stages have exponentially distributed durations. However, models that use the exponential distribution assumption (EDA) may generate biased and even misleading results in some cases. This discrepancy is particularly damaging if the models are employed to assist policy-makers in disease control and interventions. Particularly, health authorities must rely on quarantine, isolation and other non-pharmaceutical interventions to contain outbreaks of newly emerging human diseases. Models with the EDA are especially inappropriate for evaluating the effectiveness of these control strategies. This thesis includes studies of mathematical models that use more realistic assumptions on disease stage durations (with the exponential distribution as a special case). With biological parameters for SARS from the initial case series in Hong Kong and infection rates from hospitalizations in Singapore, we determined sensitivity of model results to control parameters, which allows us to compare the effectiveness of various control strategies.

Degree

Ph.D.

Advisors

Feng, Purdue University.

Subject Area

Applied Mathematics|Mathematics|Virology

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