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Volume 9, Number 5, 2019, Pages 1731-1749                                                                DOI:10.11948/20180311
Global dynamics of a Cholera model with age-of-immunity structure and reinfection
Liming Cai,Jinliang Liu,Gaoxu Fan,Huidong Chen
Keywords:Cholera model, duration time of immunity, Lyapunov functional, global stability.
Abstract:
      To understand V.Cholera transmission dynamics, in this paper, a mathematical model for the dynamics of cholera with reinfection is formulated that incorporates the duration time of the recovery individuals (age-of-immunity). The basic reproduction number $\Re_0$ for the model is identified and the threshold property of $\Re_0$ is established. By applying the persistence theory for infinite-dimensional systems, we show that the disease is uniformly persistent if the reproductive number $ \Re_0>1$. By constructing a suitable Lyapunov function, the global stability of the infection-free equilibrium in the system is obtained for $\Re_0<1$; the unique endemic equilibrium of the system is globally asymptotically stable for $\Re_0>1$.
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