一类具有时滞和扩散、含非单调发生率的传染病模型

An Epidemic Model with Delay,Diffusion and Contains Non-monotonic Incidence Rate

研究了一类具有时滞和扩散、含非单调发生率的传染病系统在Neumann边界条件下解的整体性态,采用线性化和空间分解的方法,给出了正平衡解局部稳定的充分条件,并给出了数值模拟验证.结果表明,当接触率小时,系统的正平衡解是局部渐近稳定的.

It is discussed under Neumann boundary condition that the global behavior of the solution of an epidemic system,which contains delay,diffusion and contains non-monotonic incidence rate.A sufficient condition for local stability of positive equilibrium solution is given,by using linearization and space decomposition.And numerical simulation results are also given to support the theoretical predictions.Results show that the positive equilibrium solution is locally asymptotically stable when the contact rate is small.