一类时滞SIQR传染病模型的稳定性

摘要

考虑一类具有饱和发生率的时滞SIQR传染病模型.利用特征值法,以疾病治愈周期导致的时滞为分支参数,讨论疾病平衡点的局部渐近稳定性,给出了疾病平衡点局部渐近稳定性的充分条件,并确定了模型产生局部Hopf分支的时滞临界点.仿真实例验证了所得结果的正确性.%We considered a class of delayed SIQR epidemic models with saturated incidence rate.Using the eigenvalue method,and the time delay caused by the cure cycle as the bifurcation parameter,we discussed the local asymptotic stability of the viral equilibrium,gave sufficient conditions for the local asymptotic stability of the viral equilibrium,and determined the delay critical point for the occurrence of a local Hopf bifurcation of the model.Simulation results verified the correctness of the obtained results.