Mathematical Biosciences and Engineering (MBE)


Pages: 733 - 752,    Volume: 8 ,   Issue: 3 ,       July 2011  

Stability analysis and application of a mathematical cholera model

doi:10.3934/mbe.2011.8.733          Full text: (565.3K)

Shu Liao - School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China (email)
Jin Wang - Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA 23529, United States (email)

Abstract: In this paper, we conduct a dynamical analysis of the deterministic cholera model proposed in [9]. We study the stability of both the disease-free and endemic equilibria so as to explore the complex epidemic and endemic dynamics of the disease. We demonstrate a real-world application of this model by investigating the recent cholera outbreak in Zimbabwe. Meanwhile, we present numerical simulation results to verify the analytical predictions.

Keywords: Stability, equilibrium, dynamical system, cholera model.
Mathematics Subject Classification: Primary: 34D20, 92D30.

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Received:   July   2010;   Accepted:   September  2010;   Published:   June  2011.

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