Abstract
As the first-wave COVID-19 has passed in 2020, people's awareness of self-protection began to decline gradually. How to prevent and control the second-wave COVID-19 has become an important issue in many countries and regions. By analyzing the transmission of the second-wave COVID-19 caused by an imported case in Tonghua City, Jilin Province, China, in January 2021, we establish a new mathematical COVID-19 model to simulate the transmission characteristics of the second-wave COVID-19. First, we analyze the basic properties of the model, prove the existence of the equilibrium point, and obtain the expression of the basic reproduction number with important biological significance. Secondly, we use the weighted nonlinear least square estimation method to fit the cases in Tonghua City of Jilin Province in January 2021, and get the estimated value of the parameters. The basic reproduction number of the second-wave COVID-19 in Tonghua City is R0 = 1.0695 , which is much smaller than that of the first-wave COVID-19 in Wuhan in 2020. Finally, in the optimal control part, we consider two control methods (keeping social distance and nucleic acid detection of all people in the city) to simulate the control of the disease. The results show that the control intensity of the two control methods needs to be dynamically changed and adjusted, so that the cost can be minimized with the least infection. The results of this paper can not only provide suggestions for health management departments, but also provide a reference for the analysis of the second-wave COVID-19 in other countries or regions.