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Mathematical Biosciences and Engineering

2011, Volume 8, Issue 4: 1099-1115. doi: 10.3934/mbe.2011.8.1099
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Dynamics of a delay Schistosomiasis model in snail infections

  • 1.
    Department of Mathematics and Statistics, LAMPS and CDM, York University, Toronto, ON, M3J 1P3
  • 2.
    Jiangsu Provincial Key Laboratory for NSLSCS, School of Mathematics, Nanjing Normal University, Nanjing, Jiangsu, 210046
  • 3.
    Department of Mathematics and Statistics, Laboratory of Mathematical Parallel systems (LAMPS) and CDM, York University, Toronto M3J 1P3
  • Received: 01 October 2010 Accepted: 29 June 2018 Published: 01 August 2011

  • MSC : 92D30, 37N25.

  • In this paper we modify and study a system of delay differential equations model proposed by Nåsell and Hirsch (1973) for the transmission dynamics of schistosomiasis. The modified stochastic version of MacDonald’s model takes into account the time delay for the transmission of infection. We carry out bifurcation studies of the model. The saddle-node bifurcation of the model suggests that the transmission and spread of schistosomiasis is initial size dependent. The existence of a Hopf bifurcation due to the delay indicates that the transmission can be periodic.

    Citation: Chunhua Shan, Hongjun Gao, Huaiping Zhu. Dynamics of a delay Schistosomiasis model in snail infections[J]. Mathematical Biosciences and Engineering, 2011, 8(4): 1099-1115. doi: 10.3934/mbe.2011.8.1099

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  • In this paper we modify and study a system of delay differential equations model proposed by Nåsell and Hirsch (1973) for the transmission dynamics of schistosomiasis. The modified stochastic version of MacDonald’s model takes into account the time delay for the transmission of infection. We carry out bifurcation studies of the model. The saddle-node bifurcation of the model suggests that the transmission and spread of schistosomiasis is initial size dependent. The existence of a Hopf bifurcation due to the delay indicates that the transmission can be periodic.


  • This article has been cited by:

    1. 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
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  • © 2011 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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