具双时滞和媒体影响的新冠肺炎模型的稳定性

Stability of a novel coronavirus pneumonia model with two delays and media effects

建立了具有媒体影响退化时滞和潜伏期时滞的两类易感者新冠肺炎SIR(susceptible,infective,removed)传染病模型,利用极限系统证明了系统零平衡点和无病平衡点的全局稳定性,并依次把媒体影响退化时滞、疾病潜伏时滞作为分支参数,分析了疾病平衡点局部Hopf分支的存在性.发现当把媒体影响退化时滞控制在一个左闭右开区间内时,无病平衡点全局稳定;当潜伏期时滞超过临界值时,疾病平衡点处会出现Hopf分支,新冠肺炎以周期震荡的形式存在.可见,时滞大小对模型稳定性有重要影响,媒体影响对疫情控制起到重要作用.

A novel coronavirus pneumonia SIR(susceptible,infective,removed)epidemic model with two types of susceptibility,namely,media degradation delay and latency latency,was established.The global stability of the zero equilibrium and the disease-free equilibrium of the system was systematically proved.The existence of local Hopf bifurcation of the disease equilibrium was analyzed by taking the media influence degradation delay and the disease latent delay as bifurcation parameters.It was found that the disease-free equilibrium was globally stable when the media influence degradation delay was controlled in a left closed right open interval,and when the latency delay exceeded the critical value,there would be Hopf bifurcation at the equilibrium point of the disease,the novel coronavirus pneumonia existed in the form of periodic oscillation.It was obvious that the size of time delay had an important effect on the stability of the model,the influence of the media played an important role in the control of epidemic situation.