| 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 ℜ0 for the model is identified and the threshold property of ℜ0 is established. By applying the persistence theory for infinite-dimensional systems, we show that the disease is uniformly persistent if the reproductive number ℜ0>1. By constructing a suitable Lyapunov function, the global stability of the infection-free equilibrium in the system is obtained for ℜ0<1; the unique endemic equilibrium of the system is globally asymptotically stable for ℜ0>1. |
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