一类具扩散的非线性传染病模型的分析

Analysis of an Epidemic Model with Nonlinear Incidence Rate and Diffusion

研究了一类具扩散的非线性传染病系统在Neumann边界条件下解的整体性态,通过构造Lyapunov函数给出了无病平衡点全局稳定以及染病平衡点局部稳定的充分条件.结果表明,当接触率小的时候无病平衡点是全局渐近稳定的.

Solution＇s global behavior of an epidemic system with nonlinear incidence rate and spatial diffusion is studied. A sufficient conditionfor the global asymptotical stability of disease-free equilibrium and the local asymptotical stability of endemic equilibrium is investigated by using a Lyapunov function. The results show that the disease-free equilibrium is globally asymptotically stable if the mass action coefficient is small.