MA Yan-li，NIE Dong-ming，YU Ping.Stability Research of a SIQR Model with Nonmonotone Infection Rate and Continuous Perturbations[J].Journal of Chongqing Technology and Business University(Natural Science Edition）,2021,38(2):48-55

Stability Research of a SIQR Model with Nonmonotone Infection Rate and Continuous Perturbations

DOI：

 作者 单位 马艳丽， 聂东明， 于萍 安徽新华学院 通识教育部，合肥 230088

将连续方式的接种、剔除和隔离干扰引入模型，建立了一类具有非单调传染率的SIQR传染病模型;首先，通过计算得到了疾病流行的阈值R0及无病平衡点和地方病平衡点存在的条件；其次，当R0<1时，采用Routh Hurwitz判据和极限方程理论证明了无病平衡点具有全局渐近稳定性，当R0>1时，运用Liapunov函数和LaSalle不变集原理证明了地方病平衡点E*也具有全局渐近稳定性；接着，为了进一步说明理论研究的正确性，利用Matlab软件进行了计算机模拟;最后，借助阈值R0的偏导数，对连续方式的接种、剔除和隔离策略进行了比较和分析。

Continuous vaccination，elimination and quarantine perturbations are introduced，and a SIQR epidemic model with nonmonotone infection rate is established.Firstly，the threshold R0 which determines whether the disease is extinct or not and the conditions for the existence of equilibriums are obtained by the calculation.Secondly，the globally asymptotical stability of the disease free equilibrium E0 is proved when R0<1 by means of Routh Hurwitz criterion and limit equation theory.By Liapunov function and LaSalle invariance principle，the globally asymptotical stability of the unique endemic equilibrium E* is also proved when R0>1.Thirdly，computer simulation is carried out to illustrate the correctness of the theoretical research by Matlab software.Finally，the continuous vaccination，elimination and quarantine strategies are compared and analyzed with the partial derivative of the threshold R0.