Bifurcation analysis and optimal control of an SVITR COVID model with vaccination and treatment strategies

Abstract

This study proposes and analyzes a deterministic SVITR epidemiological model describing the transmission dynamics of COVID-19 incorporating vaccination and treatment strategies. The total population is divided into susceptible, vaccinated, infected, treated, and recovered compartments. Qualitative analysis of the model is performed to determine the disease-free and endemic equilibria and the basic reproduction number. Local stability of equilibria is examined using Jacobian analysis, while global stability is investigated using Lyapunov techniques. A bifurcation analysis is carried out to examine the qualitative changes in system dynamics near the critical threshold parameter. Sensitivity analysis is performed to identify the most influential parameters affecting disease transmission. Furthermore, an optimal control framework incorporating vaccination and treatment controls is developed using Pontryagin’s Maximum Principle to minimize the number of infected individuals and intervention costs. Numerical simulations illustrate the theoretical findings and demonstrate the effectiveness of combined vaccination and treatment strategies in controlling the spread of COVID-19. The results highlight the importance of timely vaccination campaigns and effective treatment policies in mitigating epidemic outbreaks.