考虑环境病毒影响的COVID-19模型的动力学性态研究

Dynamic behaviors analysis of COVID-19 model with environmental virus effects

建立了考虑环境病毒影响的COVID-19传染病SEIARc模型,并对其进行了动力学性态分析。首先利用下一代矩阵法计算得到系统的基本再生数R_(0)^(*),进一步通过分析得到:当R_(0)^(*)<1时,无病平衡点存在且局部渐近稳定,并利用Metzler矩阵等相关理论证明了无病平衡点的全局渐近稳定性;当R_(0)^(*)>1时,系统存在唯一的地方病平衡点,且给出了地方病平衡点局部渐近稳定的条件。最后通过数值模拟发现地方病平衡点是全局渐近稳定的。研究表明,通过减少环境病毒的来源或切断传播途径,可以有效地控制COVID-19疾病的传播。

To investigate the dynamics of COVID-19 infectious disease with environmental virus effects, we establish an SEIARc model and analyse its dynamic behaviors. Firstly, the next generation matrix method is used to calculate the basic reproduction number R_(0)^(*). When R_(0)^(*)<1, the disease-free equilibrium exists and is locally asymptotically stable. Furthermore, by using of Metzler matrix and other related theories, we prove that the globally asymptotic stability of the disease-free equilibrium. When R_(0)^(*)>1, the system always has a unique endemic equilibrium, and the conditions for the locally asymptotic stability of the equilibrium of endemic diseases are given. Finally, by numerical simulation, the results of the theoretical analysis and the globally asymptotic stability of the endemic equilibrium is verified. It is shown that the transmission of COVID-19 disease can be effectively controlled by reducing the source of the environmental virus or cutting off the transmission routes.