Analyzing the infection dynamics and control strategies of cholera

Pages: 747 - 757, Issue special, November 2013

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Jianjun Paul Tian - Mathematics Department, College of William and Mary, Williamsburg, VA 23187, United States (email)
Shu Liao - School of Mathematics and Statistics, Chongqing Technology and Business University, China (email)
Jin Wang - Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA 23529, United States (email)

Abstract: We conduct a rigorous analysis for the differential equation-based cholera model proposed in [3]. Unlike traditional infectious disease SIR-type models, this model explicitly includes cholerae bacteria from the environments, and the incidence rate is a dose-dependent Michaelis-Menten type functional response. By extending the theory of monotone dynamical systems, we prove that the endemic equilibrium, when it exists, of the model is globally asymptotically stable, implying the persistence of the disease in the absence of interventions. We then modify the model by incorporating various control strategies, and study the subsequent dynamics. We find that with strong control measures, the basic reproduction number will be reduced below 1 so that the disease-free equilibrium is globally asymptotically stable. With weak controls, instead, epidemicity still occurs and a unique and globally stable endemic equilibrium state exists, though at a lower infection level and with a reduced disease outbreak growth rate. The analytical predictions are confirmed by numerical results.

Keywords:  Dose-dependent infection, cholera model, dynamical systems, global stability, disease control.
Mathematics Subject Classification:  Primary: 34D20, 92D30.

Received: July 2012; Published: November 2013.