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Volume 10, Number 2, 2020, Pages 598-623                                                                DOI:10.11948/20190006
Dynamic behavior of a delay cholera model with constant infectious period
Xue-yong Zhou,Xiang-yun Shi,Jing-an Cui
Keywords:Cholera model, permanence, stability, delay.
Abstract:
      In this paper, a delay cholera model with constant infectious period is investigated. By analyzing the characteristic equations, the local stability of a disease-free equilibrium and an endemic equilibrium of the model is established. It is proved that if the basic reproductive number $\mathcal{R}_0>1$, the system is permanent. If $\mathcal{R}_0<1$, by means of an iteration technique, sufficient conditions are obtained for the global asymptotic stability of the disease-free equilibrium. If $\mathcal{R}_0>1$, also by means of an iteration technique, sufficient conditions are obtained for the global asymptotic stability of the endemic equilibrium. Numerical simulations are carried out to illustrate the main theoretical results.
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