A vector-borne disease model with spatial diffusion with time delays and a general incidence function is studied. We derived conditions under which the system exhibits threshold behavior. The stability of the disease-free equilibrium and the endemic equilibrium are analyzed by using the linearization method and constructing appropriate Lyapunov functionals. It is shown that the given conditions are satisfied by at least two common forms of the incidence function.

中文翻译：

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具有延迟非线性发病率的媒介传播疾病模型的稳定性

研究了具有时滞空间扩散和一般发病率函数的媒介传播疾病模型。我们推导了系统表现出阈值行为的条件。利用线性化方法并构造适当的李雅普诺夫泛函，分析了无病平衡和地方病平衡的稳定性。结果表明，至少两种常见形式的关联函数满足给定条件。