具有双线性发生率的传染病模型的一般结构和研究方法

The Usual Form and Way of the Infectious Model with Bilinear Incidence

在常微分方程模型的基础上,讨论了具有空间扩散的双线性发生率传染病模型的一般结构和研究方法.通过构造Liapunov函数,并根据LaSalle不变性原理,得到了两个主要结论,证明了在一定条件下,模型的正平衡点是稳定的,最后给出例子加以论证.

On the basis of the ordinary differential equation models, we discuss the usual form and ways of studying for the infectious model which has bilinear incidence and spatial diffusion. Through structuring the Liapunov function,using the the LaSalle invariance principle,we can get two main conclusions, which proves that the positive equilibrium of the model is stable in some condition. In the end,some example is given for the proof.