Mathematical Modeling and Optimal Control of Malaria Disease Spread in North Panajam Paser Regency

Abstract

In this paper, the dynamics of malaria transmission model in Panajam Paser Utara Regency are given. The SISI (Susceptible Human-Infected Human-Susceptible Vector-Infected Vector) model is used in this paper by assuming that the human population can be infected with malaria more than once. The model parameters are estimated based on monthly cumulative data of malaria cases in Panajam Paser Utara Regency in 2023-2024 using the Kalman Filter method. The simulation results show that the comparison of the estimated value and the actual value in cases of humans infected with malaria in Panajam Paser Utara Regency in 2023-2024 produces a MAPE of 6.27% so that it can be concluded that the level of forecasting accuracy is high because it is <10%. Furthermore, two controls are considered to minimize the spread of malaria, namely human contact prevention measures with mosquitoes and mosquito spraying. Then the dynamic optimization problem is solved using the Pontryagin Minimum Principle method. The goal is to reduce the population of infected humans and mosquitoes by minimizing the costs incurred for mosquito prevention and spraying. Numerical results are presented to show that both controls can effectively minimize the spread of malaria.