An Seir Model for Measles Transmission in North Sumatra Using the Fourth-Order Runge–Kutta Method for an Optimal Control Strategy - Dwi Andini; R. Maisaroh Rezyekiyah Siregar (Universitas Cokroaminoto Palopo, 2026)
Measles remains one of the major public health concerns in North Sumatra Province. This study aims to analyze the dynamics of measles transmission using the Susceptible–Exposed–Infected–Recovered (SEIR) model, which is solved numerically using the Fourth-Order Runge–Kutta (RK4) method and incorporates a control variable to evaluate the effect of reducing social contact on disease transmission. The study employs secondary data on measles cases obtained from the North Sumatra Provincial Health Office. Numerical simulations were performed using MATLAB with a step size of h = 1 day over a simulation period of 100 days. The results show that the SEIR model is capable of describing the dynamics of measles transmission through changes in the number of individuals in each compartment. The RK4 method provides stable numerical solutions, while the implementation of the control variable effectively reduces the number of individuals in the Exposed (E) and Infected (I) compartments. Among the four control scenarios examined, namely u = 0, u = 0.3, u = 0.6, and u = 0.9, the control level of u = 0.9 was found to be the most effective in suppressing the spread of measles.