2022/09/12 by Songbai Guo, Guo, Songbai, Yuling Xue +5
Mathematics · Medicine · #34D23 #37N25 #92D30 #COVID-19 epidemiological studies #Dynamical Systems (math.DS) #FOS: Biological sciences #FOS: Mathematics #FOS: Physical sciences #Mathematical Biology Tumor Growth #Mathematical Physics (math-ph) #Mathematical and Theoretical Epidemiology and Ecology Models #Populations and Evolution (q-bio.PE)
paper · pdf · doi:10.48550/arxiv.2209.05240
openalex publication_date 2022/09/12 · openalex created_date 2022/09/14 · openalex updated_date 2026/07/28
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 V0 is globally asymptotically stable if the control reproduction number Rc<1 and globally attractive if Rc=1, which means that COVID-19 will die out; the COVID-19 equilibrium V∗ is globally asymptotically stable if Rc>1, which means that COVID-19 will be persistent. In particular, to obtain the local stability of V∗, 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∗. 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.