Asian Journal of Pure and Applied Mathematics

This study analyses a deterministic compartmental model for COVID-19 transmission that incorporates vaccination, imperfect vaccine protection, waning immunity, reinfection and booster vaccination. The population is divided into susceptible, vaccinated, exposed, infectious and recovered or booster-protected compartments. The disease-free and endemic equilibria are determined, and their stability properties are examined using the Routh-Hurwitz criterion, a matrix-based global-stability approach and a Lyapunov function with LaSalle’s invariance principle. Numerical simulations are used to compare disease dynamics without vaccination, with vaccination, at the stated critical vaccination rate, in the presence or absence of reinfection and waning immunity, and with or without booster vaccination. The analytical results indicate that the disease-free equilibrium is locally and globally asymptotically stable when the effective reproduction number is below unity, whereas persistent transmission is associated with an endemic equilibrium when the threshold exceeds unity, subject to the stated model conditions. The simulations suggest that low vaccination coverage, reinfection and loss of immunity can sustain infection within the population. Increasing vaccination coverage reduces and delays the infection peak, while booster vaccination prolongs the period during which exposed and infectious populations remain low. These findings emphasise the importance of maintaining vaccination coverage and accounting for temporary immunity and reinfection when evaluating long-term COVID-19 dynamics.