Dynamics of an SVEIR transmission model with protection awareness and two strains

As of May 2024, the main strains of COVID-19 caused hundreds of millions of infection cases and millions of deaths worldwide. In this study, we consider the COVID-19 epidemics with the main strains in the Chinese mainland. We study complex interactions among hosts, non-pharmaceutical interventions, and vaccinations for the main strains by a differential equation model called SVEIR. The disease transmission model incorporates two strains and protection awareness of the susceptible population. Results of this study show that the protection awareness plays a crucial role against infection of the population, and that the vaccines are effective against the circulation of the earlier strains, but ineffective for emerging strains. By using the next generation matrix method, the basic reproduction number of the SVEIR model is firstly obtained. Our analysis by Hurwitz criterion and LaSalle's invariance principle shows that the disease free-equilibrium point is locally and globally asymptotically stable when the threshold value is below one. The existences of endemic equilibrium points are also established, and the global asymptotic stabilities are analyzed using the Lyapunov function method. Further, the SVEIR model is confirmed to satisfy the principle of competitive exclusion, of which the strain with the larger value of the basic reproduction number is dominant. Numerically, the surveillance data with the Omicron strain and the XBB strain are split by the cubic spline interpolation method. The fitting curves against the surveillance data are plotted using the least-squares method from MATLAB. The results indicate that the XBB strain dominates in this study. Moreover, a global sensitivity analysis of the key parameters is performed by using of PRCC. The numerical simulations imply that combination control strategy positively impacts on the infection scale than what separate control strategy does, and that the earlier time producing protection awareness for the public creates less infection scale, further that the increment of protection awareness also reduces the infection scale. Therefore, the policymakers of the local government are suggested to concern the changes of protection awareness of the public.