Global Stability and Computational Analysis of a Nonlinear SIR Model with Vaccination, Waning Immunity, and Immune Boosting: Global Stability of a Nonlinear SIR Model with Vaccination

We propose and analyze a nonlinear SIR-type model incorporating vaccination,waning immunity, partial reinfection, and immune boosting within a demographi-cally regulated population. The transmission process follows a saturating incidencefunction accounting for behavioral adaptation, while the immunity dynamics dependon an infection-modulated effective waning rate. Analytical results establish well-posedness, positivity, and uniform boundedness of solutions, ensuring biologicalconsistency. The basic reproduction number Ro is derived via the next-generationmatrix method and determines the epidemic threshold. Local and global stabilityanalyses reveal that the disease-free equilibrium is globally asymptotically stablewhen Ro< 1, whereas a unique endemic equilibrium exists for Ro> 1. Numericalsimulations confirm the theoretical predictions and illustrate convergence toward theendemic equilibrium under various epidemiological conditions. The computationalanalysis highlights the combined effects of vaccination coverage, immune boosting,and partial reinfection on long-term epidemic persistence, offering quantitative in-sights for immunization strategies and disease control.