A new model of the transmission dynamics of COVID-19 propagation with vaccination and recommended treatments

Although several vaccines against COVID-19 are available for mass vaccination, non-vaccine interventions remain essential to control the pandemic, which has spread around the world due to both the imperfections of the vaccines and the emergence of new and highly transmissible variants of the virus. In this study, by developing a novel compartmental dynamic model called SVEPACR to describe the spread of the infection considering the characteristics of COVID-19, we explore how vaccination and recommended treatments (auxiliary pharmaceutical and non-pharmaceutical interventions) jointly affect COVID-19 transmission. The SVEPACR model focuses on the influence of vaccination and recommended treatments on the symptomatic and asymptomatic individuals who have incurred substantial features of COVID-19. The qualitative analysis of the proposed model is conducted, including a proof showing that the model is well-posed, the global stability of disease-free equilibrium and the unique existence of endemic equilibrium. At the same time, the model is also a good fit for real data on confirmed COVID-19 cases in Shanghai, China, in 2022. Moreover, the effective reproduction number R0 is acquired, and its sensitivity to the main model parameters is analyzed. Based on the numerical simulation of the SVEPACR model and the sensitivity analysis, the interactions between the reproduction number and the model parameters are analyzed. By introducing the concept of relative cross-infection of one compartment of the model with respect to another, the mutual influence of disease transmission between the compartments is also interpreted reasonably. The studies show that the proposed model can detect the dynamic transmission behavior of COVID-19 with a combination of vaccination and recommended treatments, proving that the recommended treatment has a higher impact on the evolution of the epidemic than vaccination alone, and advocate that this type of treatment should be consistent with the vaccination campaign in order to contain the virus.