论文标题
具有无症状感染和隔离措施的COVID-19模型的动力学
Dynamics of COVID-19 models with asymptomatic infections and quarantine measures
论文作者
论文摘要
考虑到Covid-19在不同地区的传播特征，分别进行了Covid-19的长期和短期模型的动力学分析和数值证明。长期模型致力于研究Covid-19模型的全球稳定性，该模型没有无症状的感染和隔离措施。通过使用模型和Lyapunov函数方法的限制系统，可以表明，如果控制复制号$ \ Mathcal {r} _ {c} _ {c} <1 $，并且如果$ \ \ mathcal {r} cov of yive yive of yive yive nive yive of die oiv yive of yive yive of yive of yive of yive of yive，则在全球范围均匀稳定。如果$ \ Mathcal {r} _ {c}> 1 $，则covid-19 equilibium $ v^{\ ast} $在全球渐近稳定，这意味着covid-19将是持久的。特别是，为了获得$ v^{\ ast} $的局部稳定性，我们使用矛盾和复杂模量的属性以及一些新颖的细节来证明，我们证明系统的持久性较弱，以获得$ v^{\ ast} $的全球吸引力。此外，计算相应的短期模型的最终大小，并分析其多重均衡的稳定性。 COVID-19病例的数值模拟表明，隔离措施和无症状感染对COVID-19的传播具有不可忽视的影响。
Considering the propagation characteristics of COVID-19 in different regions, the dynamics analysis and numerical demonstration of long-term and short-term models of COVID-19 are carried out, respectively. The long-term model is devoted to investigate the global stability of COVID-19 model with asymptomatic infections and quarantine measures. By using the limit system of the model and Lyapunov function method, it is shown that the COVID-19-free equilibrium $V^0$ is globally asymptotically stable if the control reproduction number $\mathcal{R}_{c}<1$ and globally attractive if $\mathcal{R}_{c}=1$, which means that COVID-19 will die out; the COVID-19 equilibrium $V^{\ast}$ is globally asymptotically stable if $\mathcal{R}_{c}>1$, which means that COVID-19 will be persistent. In particular, to obtain the local stability of $V^{\ast}$, we use proof by contradiction and the properties of complex modulus with some novel details, and we prove the weak persistence of the system to obtain the global attractivity of $V^{\ast}$. Moreover, the final size of the corresponding short-term model is calculated and the stability of its multiple equilibria is analyzed. Numerical simulations of COVID-19 cases show that quarantine measures and asymptomatic infections have a non-negligible impact on the transmission of COVID-19.
