Abstract
The global emergence of the Coronavirus (Covid-19) has resulted in far-reaching implications, encompassing substantial loss of human lives and the revelation of vulnerabilities in health systems across the globe. In response to this crisis, we revisited a prior model and extended it by incorporating a vaccination control element. This novel addition involves introducing a control factor into the vaccinated class to examine the repercussions of frequent vaccine administration as a strategic measure to mitigate the spread of COVID-19. Of particular interest in our investigation is the exploration of the criteria for the existence of numerical solutions to the model, achieved through the application of the Homotopy Perturbation Method. Our preliminary findings demonstrate that the vaccine control factor exerts substantial effects on both the susceptible and recovery classes within the model. This research contributes to the understanding of the dynamics of COVID-19 transmission, providing insights that can inform public health strategies in the ongoing global battle against the pandemic.