Electronic Thesis and Dissertation Repository


Doctor of Philosophy


Applied Mathematics


Xingfu Zou


This Ph.D thesis focuses on modeling transmission and dispersal of one of the most common infectious disease, Malaria. Firstly, an integro-differential equation system is derived, based on the classical Ross-Macdonald model, toemphasize the impacts of latencies on disease dynamics. The novelty lies in the fact that different distributionfunctions are used to describe the variance of individual latencies. The theoretical results of this projectindicate that latencies reduce the basic reproduction number. Secondly, a patch model is derived to examine how travels of human beings affects the transmission and spread of Malaria. Due to coexistence of latency and dispersal, the model turns out to be a system of delay differential equations on patches with non-local infections. The results from this work indicate that although malaria has been eradicated in many countries since the 1980s, re-emergence of the disease is possible, and henceprecautionary measures should be taken accordingly. Thirdly, since there are more than five species of Malaria Plasmodium causing human malaria, and they are currently distributed in different geographic regions, co-invasion by multiple species of malaria may arise. We propose multi-species models to explore co-infection at within-host level and co-existence at the between-host level. The analysis shows that competition exclusion dominates at the within-host level, meaning that longterm co-infection of a single host by multiple species can be generically excluded. However, at thebetween-host level, long term co-existence of multiple species in a region is possible.