Dynamics and strategies evaluations of a novel reaction-diffusion COVID-19 model with direct and aerosol transmission

Yunbo Tu; Xinzhu Meng; Shujing Gao; Tasawar Hayat; Aatef Hobiny

doi:10.1016/j.jfranklin.2022.09.022

Dynamics and strategies evaluations of a novel reaction-diffusion COVID-19 model with direct and aerosol transmission

J Franklin Inst. 2022 Nov;359(17):10058-10097. doi: 10.1016/j.jfranklin.2022.09.022. Epub 2022 Oct 1.

Authors

Yunbo Tu¹, Xinzhu Meng^{1

2}, Shujing Gao³, Tasawar Hayat^{2

4}, Aatef Hobiny²

Affiliations

¹ College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, PR China.
² Nonlinear Analysis and Applied Mathematics(NAAM)-Research Group, Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia.
³ Key Laboratory of Jiangxi Province for Numerical Simulation and Emulation Techniques, Gannan Normal University, Ganzhou 341000, China.
⁴ Department of Mathematics, Quaid-i-Azam University 45320, Isamabad 44000, Pakistan.

Abstract

The COVID-19 epidemic has infected millions of people and cast a shadow over the global economic recovery. To explore the epidemic's transmission law and provide theoretical guidance for epidemic prevention and control. In this paper, we investigate a novel SEIR-A reaction-diffusion COVID-19 system with direct and aerosol transmission. First, the solution's positivity and boundedness for the system are discussed. Then, the system's the basic reproduction number is defined. Further, the uniform persistence of disease when $R_{0} > 1$ is explored. In addition, the system equilibrium's global stability based on $R_{0}$ is demonstrated. Next, the system's NSFD scheme is investigated and the discrete system's positivity, boundedness, and global properties are studied. Meantime, global sensitivity analysis on threshold $R_{0}$ is investigated. Interestingly, the effects of three strategies, including vaccination, receiving treatment, and wearing a mask, are evaluated numerically. The results suggest that the above three strategies can effectively control the peak and final scale of infection and shorten the duration of the epidemic. Finally, theoretical simulations and instance predictions are used to give several key indicators of the epidemic, including threshold $R_{0}$ , peak, time to peak, time to clear cases, and final size. The instance prediction results are as follows: (1) The basic reproduction numbers of Yangzhou and Putian in China are $R_{0} = 2.5107$ and $R_{0} = 1.8846$ , respectively. (2) This epidemic round in Yangzhou will peak at 56 new daily confirmed cases on the 9th day (August 5), and Putian will peat at 37 new daily confirmed cases on the 6th day (September 15). (3) The final scale of infections in Yangzhou and Putian reached 570 and 205 cases, respectively. (4) The Yangzhou epidemic is expected to be completely cleared on the 25th day (August 21). In addition, the Putian epidemic will continue for 15 days and be cleared on September 24. The analysis results mean that we should improve our immunity by actively vaccinating, reducing the possibility of aerosol transmission by wearing masks. In particular, people should maintain proper social distance, and the government should strengthen medical investment and COVID-19 project research.