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

Pino-Romero N.; Haya-Enríquez E.F. · Proyecciones (2026) · DOI: 10.22199/issn.0717-6279-7082

Resumen

We propose and analyze a nonlinear SIR-type model incorporating vaccination, waning immunity, partial reinfection, and immune boosting within a demographically regulated population. The transmission process follows a saturating incidence function accounting for behavioral adaptation, while the immunity dynamics depend on an infection-modulated effective waning rate. Analytical results establish well-posedness, positivity, and uniform boundedness of solutions, ensuring biological consistency. The basic reproduction number R0 is derived via the next-generation matrix method and determines the epidemic threshold. Local and global stability analyses reveal that the disease-free equilibrium is globally asymptotically stable when R0 < 1, whereas a unique endemic equilibrium exists for R0 > 1. Numerical simulations confirm the theoretical predictions and illustrate convergence toward the endemic equilibrium under various epidemiological conditions. The computational analysis highlights the combined effects of vaccination coverage, immune boosting, and partial reinfection on long-term epidemic persistence, offering quantitative insights for immunization strategies and disease control.

Instituciones: Universidad Peruana Cayetano Heredia; Universidad Continental