Dinamika Solusi dan Kontrol Optimal Model Penyakit ISPA di Kota Malang - Lukman Hakim (Limits: Journal of Mathematics and Its Applications, 2025)
The current research provides a mathematical model utilizing nonlinear ordinary differential equations to represent the spread of acute respiratory infections (ARI). The model is divided into five compartments: the susceptible population, the vaccinated population, the latent population, the infected population, and the recovered population. Through dynamic analysis, two equilibrium points were determined. The disease-free equilibrium point is stable under conditions, while the endemic equilibrium point exhibits asymptotic stability. The lsqcurvefit methods was implemented to estimate the parameters, facilitating accurate parameter approximation. The acquisition of estimated values was implemented in the sensitivity analysis, and several parameters sensitive to were obtained: the vaccination rate, the natural death rate, the mortality cause infection rate, and recovery rate. An optimal control problem was designed by incorporating two control variables: firstly, reducing the direct contact between the susceptible and infected populations, and the other focused on increasing the intensity of infected individuals. The solution of optimal control problem was derived using Pontryagin's Principle. The objective function was formulated as a Lagrange to minimize the number of latent and infected individuals, and maximizing the vaccinated and recovered populations. Finally, numerical simulations were performed to validate the theoretical analysis, demonstrating that the results in line with the objective function of optimal control and effectively support the proposed strategies for controlling the disease.