| Dynamic behavior of a delay cholera model with constant infectious period |
| Xueyong 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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