Analisis Dinamik Model Infeksi Mikrobakterium Tuberkulosis Dengan Dua Lokasi Pengobatan

Abstract

Tuberculosis is an infectious disease caused by Mycobacterium tuberculosis. The disease is considered dangerous because it infects the lungs and other organs of the body and can lead to death. This study discusses a mathematical model for the spread of tuberculosis with two treatment sites as an effort to reduce the transmission rate of TB cases. Treatment for TB patients can be done at home and in hospitals. The purpose of this study was to construct a mathematical model and analyze the qualitative behavior of the TB spread model. The construction of the model uses the SEIR epidemic model which is divided into five subpopulations, namely susceptible subpopulations, latent subpopulations, infected subpopulations receiving treatment at home, and infected subpopulations receiving treatment at the hospital, and cured subpopulations. The analysis of qualitative behavior in the model includes determining the local and global equilibrium and stability points. The results of the analysis shows that the model has two equilibrium points, namely a disease-free equilibrium point and the endemic equilibrium point. The existence of endemic equilibrium point and the local and global stability of the two equilibrium points depend on the basic reproduction number denoted by . If ,  there is only disease-free equilibrium point. If , there are two equilibrium points, namely the disease-free equilibrium point and the endemic equilibrium point. Stability analysis shows that the disease-free equilibrium point is locally and globally asymptotically stable if . While, if , the endemic equilibrium point will be asymptotically stable locally and globally.