In this paper,unlike traditional infectious disease SIR-type models,this model explicitly includes cholerae bacteria from the environments and time delay.In this paper,we study the disease-free equilibrium is globally asymptotically stable by Lyapunov functional when the basic reproductive number R0 ＜ 1.Furthermore,when R0 ＞ 1,we prove the positive equilibrium is locally asymptotically stable and permanent.
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