In this note, we consider a multi-strain cholera model with an imperfect vaccine. First, the existence and uniqueness of the endemic equilibrium of the model is proved. In addition, by constructing suitable Lyapunov function and using LaSalle’s invariance principle, it is proven that the endemic equilibrium of the model is globally asymptotically stable in a special case. This partially verifies the conjecture put forward by Safi et al. (2013).

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关于疫苗不完善的多株霍乱模型的全局稳定性的说明

在本说明中，我们考虑了一个带有不完善疫苗的多菌株霍乱模型。首先，证明了模型的地方性均衡的存在性和唯一性。此外，通过构造合适的Lyapunov函数，利用LaSalle不变原理，证明了模型的地方性均衡在特殊情况下是全局渐近稳定的。这部分验证了 Safi 等人提出的猜想。（2013）。