Backward bifurcation is an important property of infectious disease models. A centre manifold method has been developed by Castillo-Chavez and Song for detecting the presence of backward bifurcation and deriving a necessary and sufficient condition for its occurrence in Ordinary Differential Equations (ODE) models. In this paper, we extend this method to partial differential equation systems. First, we state a main theorem. Next we illustrate the application of the new method on a chronological age-structured Susceptible-Infected-Susceptible (SIS) model with density-dependent recovery rate, an age-since-infection structured HIV/AIDS model with standard incidence and an age-since-infection structured cholera model with vaccination.

向后分叉是传染病模型的重要属性。Castillo-Chavez和Song开发了一种中心流形方法，用于检测反向分叉的存在并推导其在常微分方程（ODE）模型中发生的必要条件和充分条件。在本文中，我们将此方法扩展到偏微分方程组。首先，我们陈述一个主要定理。接下来，我们将说明该新方法在具有密度依赖性恢复率的按时间顺序排列的年龄结构敏感性感染-易感性（SIS）模型，具有标准发病率和年龄的年龄-自感染结构的HIV / AIDS模型中的应用疫苗接种的感染性霍乱模型。