Evaluating vaccination and quarantine for measles intervention strategy in Jakarta, Indonesia through mathematical modeling

Abstract

This article introduces a system of seven-dimensional nonlinear differential equations to analyze the influence of vaccination strategies on the spread of measles in Jakarta, using weekly incidence data for parameter estimation. Our dynamical analysis begins by determining the existence and stability of equilibrium states and calculating the basic reproduction number, denoted by $R_0$. The analysis indicates that the disease-free equilibrium is globally asymptotically stable if $R_0<1$. Conversely, the endemic equilibrium always persists and remains stable if $R_0>1$. Next, we conduct a global sensitivity analysis using the Partial Rank Correlation Coefficient (PRCC) method integrated with Latin Hypercube Sampling (LHS). The results indicate that the initial-dose vaccination intervention plays the most critical role in reducing the reproduction number, highlighting its significant potential as a measles control strategy. Additionally, we extend the model into an optimal control problem framework to identify the most effective strategy for preventing measles spread while minimizing intervention costs. This control optimization is formulated using Pontryagin’s Maximum Principle and solved numerically through the forward–backward sweep method. The cost-effectiveness analysis indicates that a combination of vaccination and quarantine is the most effective strategy compared to other possible control measures.