Abstract
•A multi-objective optimal reaction-diffusion model based on vaccination-isolation strategy is proposed.•Complex dynamic behaviors of the reaction-diffusion model are explored.•The functions of social cost, social benefit, and basic reproduction number are given.•The optimal path of COVID-19 control based on the basic reproduction number is determined.•The optimization of social cost, social benefit and basic reproduction number, based on vaccination-isolation is explored.
In this paper, a reaction-diffusion COVID-19 model is proposed to explore how vaccination-isolation strategies affect the development of the epidemic. First, the basic dynamical properties of the system are explored. Then, the system’s asymptotic distributions of endemic equilibrium under different conditions are studied. Further, the global sensitivity analysis of R0 is implemented with the aim of determining the sensitivity for these parameters. In addition, the optimal vaccination-isolation strategy based on the optimal path is proposed. Meantime, social cost C(m,σ), social benefit B(m,σ), threshold R0(m,σ) three objective optimization problem based on vaccination-isolation strategy is explored, and the maximum social cost (MSC) and maximum social benefit (MSB) are obtained. Finally, the instance prediction of the Lhasa epidemic in China on August 7, 2022, is made by using the piecewise infection rates β1(t), β2(t), and some key indicators are obtained as follows: (1) The basic reproduction numbers of each stage in Lhasa, China are R0(1:8)=0.4678,R0(9:20)=2.7655,R0(21:30)=0.3810 and R0(31:100)=0.7819; (2) The daily new cases of this epidemic will peak at 43 on the 20th day (August 26, 2022); (3) The cumulative cases in Lhasa, China will reach about 640 and be cleared about the 80th day (October 28, 2022). Our research will contribute to winning the war on epidemic prevention and control.