ANALISIS DINAMIKA DAN KESTABILAN MODEL SIR DAN SEIR PADA PENYEBARAN TUBERKULOSIS DI KOTA PONTIANAK

Abstract

This study aims to analyze the transmission dynamics of Tuberculosis (TB) in Pontianak City in 2024 using the SIR and SEIR models to evaluate system stability and disease transmission potential. The methodology involves formulating systems of differential equations, determining equilibrium points, performing local stability analysis using the Jacobian matrix, and calculating the basic reproduction number as an epidemiological threshold parameter. The epidemiological parameters and population data used were obtained from the 2024 West Kalimantan Health Profile as an official data source, which were subsequently normalized into population proportions. To verify the analytical results, numerical simulations were conducted using Python. The findings indicate that the basic reproduction number in both models is less than one, implying that the system converges to the disease-free equilibrium and that the infection cannot sustain long-term transmission. Numerical results show that the proportions of infected and exposed individuals gradually decline to zero. Furthermore, simulations of the SEIR model with the initial condition produce dynamics identical to the SIR model, confirming that SEIR extends SIR when the latent compartment is considered. These results demonstrate that mathematical modeling provides a quantitative framework for understanding TB dynamics and supports the evaluation of disease control strategies based on epidemiological parameters.