Mathematical Biosciences and Engineering (MBE)

Dynamics of a delay Schistosomiasis model in snail infections

Pages: 1099 - 1115, Volume 8, Issue 4, October 2011      doi:10.3934/mbe.2011.8.1099

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Chunhua Shan - Department of Mathematics and Statistics, LAMPS and CDM, York University, Toronto, ON, M3J 1P3, Canada (email)
Hongjun Gao - Jiangsu Provincial Key Laboratory for NSLSCS, School of Mathematics, Nanjing Normal University, Nanjing, Jiangsu, 210046, China (email)
Huaiping Zhu - Department of Mathematics and Statistics, Laboratory of Mathematical Parallel systems (LAMPS) and CDM, York University, Toronto M3J 1P3, Canada (email)

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.

Keywords:  Schistosomiasis, time delay, stability, saddle-node bifurcation, Hopf bifurcation.
Mathematics Subject Classification:  92D30, 37N25.

Received: October 2010;      Accepted: May 2011;      Available Online: August 2011.