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SVIR Model Analysis of Measles with Incomplete Vaccination and 1 Waning Immunity: Sidoarjo-Indonesia Case
Abstract
Measles remains a significant public health challenge in Indonesia, especially in regions
with heterogeneous vaccination coverage and waning immunity. This study develops and
analyzes a Susceptible–Vaccinated–Infected–Recovered (SVIR) compartmental model for
measles transmission in Sidoarjo City, Indonesia, incorporating waning immunity. The basic
reproduction number R0 is derived using the next-generation matrix method, and the global
stability of both the disease-free and endemic equilibria is rigorously proven via Lyapunov
functions. Model parameters are estimated from weekly 2023 surveillance data in Sidoarjo City
using Particle Swarm Optimization (PSO), Extended Kalman Filter, Maximum Likelihood
Estimation, and Least Squares, and evaluated via Mean Absolute Percentage Error (MAPE).
PSO achieves the lowest MAPE (11.17%), outperforming the other methods. The estimated
R0 = 0.668confirms a disease-free regime. Normalized sensitivity analysis identifies vaccine
efficacy as the most influential parameter; a decline in efficacy to0 .75elevates R0 close to
the critical threshold, and any further reduction pushes the system into an endemic state.
These findings underscore the necessity of maintaining high vaccine efficacy through booster
programs and strengthened immunization strategies to sustain measles elimination at the
district level.
Keywords
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DOI: https://doi.org/10.18860/cauchy.v11i2.43842
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