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Mathematical Biosciences and Engineering

2008, Volume 5, Issue 3: 505-522. doi: 10.3934/mbe.2008.5.505
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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
  • Received: 01 June 2007 Accepted: 29 June 2018 Published: 01 June 2008

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

  • 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.

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

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  • 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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    2. Robert C. Spear, Shuo Wang, Exploring the Contribution of Host Susceptibility to Epidemiological Patterns of Schistosoma japonicum Infection Using an Individual-Based Model, 2015, 92, 0002-9637, 1245, 10.4269/ajtmh.14-0691
    3. M. A. Aziz-Alaoui, Jean M.-S. Lubuma, Berge Tsanou, Prevalence-based modeling approach of schistosomiasis: global stability analysis and integrated control assessment, 2021, 40, 2238-3603, 10.1007/s40314-021-01414-9
    4. Ruijun Zhao, Fabio Augusto Milner, A Mathematical Model of Schistosoma mansoni in Biomphalaria glabrata with Control Strategies, 2008, 70, 0092-8240, 1886, 10.1007/s11538-008-9330-5
    5. S. Mushayabasa, C. P. Bhunu, Modeling Schistosomiasis and HIV/AIDS Codynamics, 2011, 2011, 1748-670X, 1, 10.1155/2011/846174
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