Comprehensive analysis of COVID-19 transmission dynamics: mathematical modeling, stability analysis, and optimal control strategies

Abstract

Abstract This paper presents a mathematical model for comprehensively analyzing the transmission dynamics of COVID-19. We investigate the model’s various properties, such as positivity, boundedness, and the existence and uniqueness of solutions. Additionally, we calculate the basic reproductive number, denoted as R 0, to gauge the epidemic’s potential spread. Furthermore, we conduct a stability analysis to understand the long-term behavior of the model. Furthermore, we devised an optimal control strategy to effectively curb disease transmission. Using graphical analysis, we assess the impact of secondary infection rates and quarantine rates across different population groups. Finally, we compare our proposed numerical scheme with the well-known RK-4 scheme, emphasizing the NSFD scheme’s ability to maintain positivity, unlike the RK-4 scheme. Our numerical simulations offer strong evidence supporting the theoretical findings, demonstrating the effectiveness of our results.