Mathematical modeling of vaccination as a control measure of stress to fight COVID-19 infections

Abstract

The world experienced the life-threatening COVID-19 disease worldwide since its inversion. The whole world experienced difficult moments during the COVID-19 period, whereby most individual lives were affected by the disease socially and economically. The disease caused millions of illnesses and hundreds of thousands of deaths worldwide. To fight and control the COVID-19 disease intensity, mathematical modeling was an essential tool used to determine the potentiality and seriousness of the disease. Due to the effects of the COVID-19 disease, scientists observed that vaccination was the main option to fight against the disease for the betterment of human lives and the world economy. Unvaccinated individuals are more stressed with the disease, hence their body’s immune system are affected by the disease. In this study, the $SVEIHR$ deterministic model of COVID-19 with six compartments was proposed and analyzed. Analytically, the next-generation matrix method was used to determine the basic reproduction number ( $R_0$ ). Detailed stability analysis of the no-disease equilibrium ( $E_0$ ) of the proposed model to observe the dynamics of the system was carried out and the results showed that $E_0$ is stable if $R_0<1$ and unstable when $R_0>1$ . The Bayesian Markov Chain Monte Carlo (MCMC) method for the parameter identifiability was discussed. Moreover, the sensitivity analysis of $R_0$ showed that vaccination was an essential method to control the disease. With the presence of a vaccine in our $SVEIHR$ model, the results showed that $R_0=0.208$ , which means COVID-19 is fading out of the community and hence minimizes the transmission. Moreover, in the absence of a vaccine in our model, $R_0=1.7214$ , which means the disease is in the community and spread very fast. The numerical simulations demonstrated the importance of the proposed model because the numerical results agree with the sensitivity results of the system. The numerical simulations also focused on preventing the disease to spread in the community.