Mathematical modeling of host-parasite dynamics
Abstract
This thesis studies biological and public health questions associated with host-parasite interactions using mathematical models that consist of ordinary and partial differential equations. A particular host-parasite system, the human-schistosome-snail system, is considered and the specific questions addressed include the impact of age-dependent infection rate of human hosts on treatment strategies and the role of drug treatment of humans in the development of resistant strains of parasites. Another model with two types of hosts and two strains of parasites is also studied in a more general setting to investigate how heterogeneities in parasite virulence and host life-history may affect the persistence and spread of disease. To study the problem of age-dependent treatment strategy for schistosomiasis, we consider two models that are systems of partial differential equations. One model includes a single parasite strain and the other model includes both drug-sensitive and drug-resistant strains. These models incorporate both the human hosts and the intermediate snail hosts. Human hosts have an age-dependent infection rate and the snail hosts have an infection-age-dependent cercaria releasing rate. A detailed analysis is provided for the one-strain model. Some of the results for the one-strain model are expanded to the two-strain model, and the threshold condition for the coexistence of both strains is derived. In the model with two types of hosts and two strains of parasites, we focus on the impact of coinfection on the host-parasite interaction when the two types of hosts have different susceptibilities to the two parasite strains and employ different defensive mechanisms. We assume that the parasites will evolve to maximize their "invasion" reproductive number. Our results show that coexistence driven by coinfection is possible even when the reproductive number of one strain is below 1. We identify conditions that determine the evolution of parasite specialism or generalism based on the life-history strategies employed by hosts and investigate how host strains may influence parasite persistence.
Degree
Ph.D.
Advisors
Feng, Purdue University.
Subject Area
Mathematics|Parasitology
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