Analysis of COVID-19 epidemic transmission trend based on a time-delayed dynamic model

Abstract

Based on the control strategies, transmission mechanism and clinical progression of COVID-19, we propose a compartmental model with time delays. Two time delays are introduced into the model to describe the incubation period of the disease and the quarantine period of uninfected individuals who have contacts with infected people. In order to reveal the spread rule for COVID-19, we study the threshold dynamics for the model. The basic reproduction number \\begin{document}$ \\mathcal R_0 $\\end{document} is obtained. When \\begin{document}$ \\mathcal R_0 , the disease-free equilibrium is locally asymptotically stable, when \\begin{document}$ \\mathcal R_0>1 $\\end{document} , the disease-free equilibrium is unstable and the disease is uniformly persistent. As the model s applications, we study COVID-19 transmission in the United States. The parameters are chosen to fit public data in the US. The numerical results indicate that an outbreak peak time in the US will appear in the middle of March. Sensitive analysis results show that enhancing the control measures, such as keeping social distance, wearing masks, isolation etc., can significantly contribute to the prevention and control of COVID-19 infection.