This paper investigates global dynamics of an infection age-space structured cholera model. The model describes the vibrio cholerae transmission in human population, where infection-age structure of vibrio cholerae and infectious individuals are incorporated to measure the infectivity during the different stage of disease transmission. The model is described by reaction–diffusion models involving the spatial dispersal of vibrios and the mobility of human populations in the same domain Ω ⊂ ℝn. We first give the well-posedness of the model by converting the model to a reaction–diffusion model and two Volterra integral equations and obtain two constant equilibria. Our result suggest that the basic reproduction number determines the dichotomy of disease persistence and extinction, which is achieved by studying the local stability of equilibria, disease persistence and global attractivity of equilibria.

本文研究了感染年龄空间结构霍乱模型的全局动态。该模型描述了霍乱弧菌在人群中的传播，其中结合了霍乱弧菌和传染性个体的感染年龄结构，以测量疾病传播不同阶段的传染性。该模型由反应扩散模型描述，该模型涉及弧菌的空间扩散和同一域 Ω ⊂ ℝ n中人口的流动性. 我们首先通过将模型转换为反应扩散模型和两个沃尔泰拉积分方程来给出模型的适定性，并获得两个常数平衡。我们的研究结果表明，基本繁殖数决定了疾病持续和灭绝的二分法，这是通过研究平衡的局部稳定性、疾病持续性和平衡的全局吸引力来实现的。