Abstract
<jats:p>Measles remains a significant public health challenge in Indonesia, especially in regionswith heterogeneous vaccination coverage and waning immunity. This study develops andanalyzes a Susceptible–Vaccinated–Infected–Recovered (SVIR) compartmental model formeasles transmission in Sidoarjo City, Indonesia, incorporating waning immunity. The basicreproduction number R0 is derived using the next-generation matrix method, and the globalstability of both the disease-free and endemic equilibria is rigorously proven via Lyapunovfunctions. Model parameters are estimated from weekly 2023 surveillance data in Sidoarjo Cityusing Particle Swarm Optimization (PSO), Extended Kalman Filter, Maximum LikelihoodEstimation, and Least Squares, and evaluated via Mean Absolute Percentage Error (MAPE).PSO achieves the lowest MAPE (11.17%), outperforming the other methods. The estimatedR0 = 0.668confirms a disease-free regime. Normalized sensitivity analysis identifies vaccineefficacy as the most influential parameter; a decline in efficacy to0 .75elevates R0 close tothe critical threshold, and any further reduction pushes the system into an endemic state.These findings underscore the necessity of maintaining high vaccine efficacy through boosterprograms and strengthened immunization strategies to sustain measles elimination at thedistrict level.</jats:p>