一类具有隔离项的时滞分数阶SIQ传染病模型的稳定性分析

摘要:为了探讨引入时滞对分数阶模型稳定性的影响,建立了一类具有隔离项的时滞分数阶SIQ传染病模型.首先,计算了模型的特征矩阵和特征方程,求出了模型的基本再生数和平衡点; 其次,在无时滞和有时滞两种情况下给出了具有隔离项的分数阶SIQ传染病模型存在无病平衡点稳定的充分条件; 最后,利用分岔理论对模型出现的Hopf分岔行为进行了分析,结果表明模型的动力学特性与引入时滞的阈值大小密切相关.

Stability analysis of a class of time - lagged fractional - order SIQ infectious disease models with segregation

In order to explore the effect of introducing time lags on the stability of the fractional - order model, we developed a kind of time - lagged fractional SIQ infectious disease models with isolation terms.Firstly, we calculated the characteristic matrix and characteristic equation of the model, and we finded the basic regenerative number and equilibrium point of the model.Secondly, we provided sufficient conditions for a stable disease - free equilibrium of the model in the cases of no time lag and with time lag.Finally, by using the bifurcation theory, we analyzed the Hopf bifurcation behavior of the model.The results showed that the dynamic properties of the model were closely related to the threshold size when introducing time lags.