Periodic solution of a stochastic SIQR epidemic model incorporating media coverage

In this paper, we propose a stochastic SIQR epidemic model with periodic parameters and media coverage. Firstly, we study that the stochastic non-autonomous periodic system has a unique global positive solution. Secondly, by using the Khasminskii's theory, we prove that this stochastic periodic system has a nontrivial positive periodic solution. Then, we obtain the sufficient condition for extinction of the disease. Finally, numerical simulations are employed to illustrate our theoretical analysis.

本文提出了一个具有周期参数和媒体报道的随机SIQR传染病模型。首先，我们研究发现该随机非自治周期系统存在唯一的全局正解。其次，运用哈斯明斯基理论，我们证明了这个随机周期系统存在一个非平凡的正周期解。接着，我们得出了疾病灭绝的充分条件。最后，通过数值模拟对我们的理论分析进行了验证。