Xiao,Yanyu. 2011. Study of Malaria Transmission Dynamics by Mathematical Models. Doctoral thesis. The Unversity of Western Ontario.
Abstract: This Ph.D thesis focuses on modeling transmission and dispersal of one of the most common infectious diseases, malaria.
Firstly, an integro-differential equation system is derived, based on the classical Ross-Macdonald model, to emphasize the impact of the disease latency on disease dynamics. The novelty lies in the fact that different distribution functions are used to describe the variance of individual latencies. The theoretical results of this project indicate that latencies reduce the basic reproduction number.
Secondly, a patch model is derived to examine how traveling by 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 suggest that although malaria has been eradicated in many countries since the 1980s, re-emergence of the disease is still possible, and hence precautionary measures should be taken accordingly.
Thirdly, since there are more than five species of malaria parasites causing human malaria, and these are currently distributed in different geographic regions, co-invasion by multiple strains of malaria may arise. We propose multi-strain models to explore co-infection at the within-host level and co-existence at the between-host level. The analysis shows that competitive exclusion dominates at the within-host level, meaning that long term co-infection of a single host by multiple strains can be generically excluded. However, at the between-host level, long term co-existence of multiple strains in a region is possible.
Keywords: Infectious disease, malaria, latency, spatial dispersal, multi-species, mathematical modeling, differential equations, model
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