COVID-19 REINFECTION PROCESSES: MATHEMATICAL MODELING, DATA FITTING WITH TIME-VARYING PARAMETERS, AND OPTIMAL CONTROL STUDIES

In this paper, we construct a COVID-19 dynamic model that included both the initial and reinfected population compartments, and conduct a structural identifiability analysis of the model parameters to ensure the robustness of the parameter fitting results. We use some actual statistical data from North Carolina to fit the model and estimate the values of some important parameters. In order to accurately fit the parameters in the model, we improve the physics-informed neural networks (PINNs) method in this paper, so that the fitting results can be reproduced on Matlab. The results of this study show that the transmission capacity of the virus in the reinfected person is only slightly lower than that of the first infected person, and vaccination is not effective in reducing the transmission rate of the virus. The death rate of the reinfected is much higher than that of the first infected person. Finally, we conduct a cost-effectiveness study using optimal control methods and found that, while it is easier to reduce reinfection by combining multiple strategies, the most effective strategy for reducing reinfection is to increase treatment cure rates and reduce direct or indirect contact among those who have recovered.