Dynamics of a delay Schistosomiasis model in snail infections

Chunhua Shan; Hongjun Gao; Huaiping Zhu; Chunhua Shan; Hongjun Gao; Huaiping Zhu

doi:10.3934/mbe.2011.8.1099

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.
- time delay,
- stability,
- Hopf bifurcation.,
- saddle-node bifurcation,
- Schistosomiasis
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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Abstract

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.
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