This paper provides an analysis on global dynamics of a diffusive cholera model. We formulate the model by a reaction–diffusion system with space-dependent parameters and bacterial hyperinfectivity, where susceptible and infectious humans disperse with distinct dispersal rates and the hyper-infectious and lower-infectious vibrios in contaminated water are assumed to be immobile in the domain. We first establish the well-posedness of the model. To cope with the lack of compactness of solution semiflow, we verify the asymptotic smoothness of semiflow implied with \(\kappa \)-contraction condition. The basic reproduction number, \(\mathfrak {R}_0\), is identified as a threshold, predicting whether or not the disease extinction and persistence will occur. \(\mathfrak {R}_0\) is also equivalently characterized by some principle spectral conditions of an associated elliptic eigenvalue problem. The asymptotic profiles of the positive steady state are investigated for the cases when the dispersal rate of the susceptible humans is small and large. Our theoretical results indicate that: (1) cholera epidemics will be extinct through restricting the flow of susceptible humans within some extend; (2) the risk of infection will be underestimated if hyperinfectivity is not considered. In a homogeneous case, we also confirm the global attractivity of a unique positive equilibrium by utilizing the technique of Lyapunov function.

本文提供了扩散霍乱模型的整体动力学分析。我们通过具有空间依赖参数和细菌高感染性的反应扩散系统来建立模型，其中易感和感染性人类以不同的分散速率分散，并且假定高感染性和低感染性弧菌在污染域中是不可移动的。我们首先建立模型的适定性。为了解决溶液半流的紧度不足的问题，我们验证了\（\ kappa \） -收缩条件所隐含的半流的渐近光滑度。基本繁殖数\（\ mathfrak {R} _0 \）被确定为一个阈值，预测是否会发生疾病的灭绝和持久性。\（\ mathfrak {R} _0 \）同样由相关的椭圆特征值问题的一些主要频谱条件表征。对于易感人群的扩散速度较小和较大的情况，研究了正稳态的渐近曲线。我们的理论结果表明：（1）霍乱的流行将在一定程度上限制易感人群的流动，从而使其灭绝；（2）如果不考虑过度感染，那么感染的风险就会被低估。在同质情况下，我们还利用Lyapunov函数技术确定了唯一正平衡的全局吸引性。