Mathematical Biosciences and Engineering, 2008, 5(3): 505-522. doi: 10.3934/mbe.2008.5.505.

Primary: 92D30, 92D40; Secondary: 93C15, 93C20.

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A deterministic model of schistosomiasis with spatial structure

1. Department of Mathematics, Purdue University, 150 North University Street, West Lafayette, IN 47907-2067

It has been observed in several settings that schistosomiasis is less prevalent in segments of river with fast current than in those with slow current. Some believe that this can be attributed to flush-away of intermediate host snails. However, free-swimming parasite larvae are very active in searching for suitable hosts, which indicates that the flush-away of larvae may also be very important. In this paper, the authors establish a model with spatial structure that characterizes the density change of parasites following the flush-away of larvae. It is shown that the reproductive number, which is an indicator of prevalence of parasitism, is a decreasing function of the river current velocity. Moreover, numerical simulations suggest that the mean parasite load is low when the velocity of river current flow is sufficiently high.
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Keywords delay differential equations.; reproductive numbers; schistosomiasis

Citation: Fabio Augusto Milner, Ruijun Zhao. A deterministic model of schistosomiasis with spatial structure. Mathematical Biosciences and Engineering, 2008, 5(3): 505-522. doi: 10.3934/mbe.2008.5.505


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