Optimal Control and Model Analysis of The Spread of Pneumonia in Toddlers in East Java-Indonesia Using The Pontryagin’s Minimum Principle - Widodo, Basuki; Kamiran, Kamiran; Syahputri, Denisa Dwi (Department of Mathematics, Universitas Negeri Gorontalo, 2025)
Pneumonia is a type of acute respiratory infection (ARI) that attacks the lungs and is caused by various microorganisms, such as bacteria, viruses, parasites, fungi, exposure to chemicals, or physical damage to the lungs. Pneumonia is included in the list of 10 diseases with the highest number of cases according to the Indonesian Ministry of Health reported in April 2023. Pneumonia is the biggest cause of death in toddlers aged 12-59 months, reaching 12.5%. Therefore, to reduce the spread of pneumonia, this research will discuss providing optimal control using the mathematical model of SEIR (Susceptible-Exposed-Infected-Recovered). The model used is a pneumonia spreading model with implementing control in the form of first stage treatment and second stage treatment. The results of the stability analysis show that at the disease-free equilibrium point and the endemic equilibrium point, the system is stable respectively. Based on controllability analysis, it is obtained that the system is controlled so that the system can be controlled. In addition, based on the results of the analysis of the optimal control problem with Pontryagin’s Minimum Principle simulated with Runge Kutta order 4, it shows that the first stage of treatment control (u1) and the second stage of treatment (u2) are very effective in reducing the number of individuals infected with mild pneumonia and severe pneumonia respectively.