Bifurkasi Mundur dalam Model Matematika Penyebaran Penyakit Tuberkulosis dengan Mempertimbangkan Laju Deteksi dan Pengobatan

Chrissytalia Finka Liantoko (Program Studi Matematika, Fakultas Sains dan Teknologi, Universitas Sanata Dharma, Yogyakarta 55281, Indonesia)
Lusia Krismiyati Budiasih (Program Studi Matematika, Fakultas Sains dan Teknologi, Universitas Sanata Dharma, Yogyakarta 55281, Indonesia)

Mathematical Sciences and Applications Journal
Vol. 4 No. 1 (2023): Mathematical Sciences and Applications Journal

Tuberculosis is a disease caused by the bacteria Mycobacterium tuberculosis. This disease can spread bacteria from one individual to another. In this article, we analyzed the spread of Tuberculosis using the SEIR model. The mathematical model is presented in a system of first-order nonlinear ordinary differential equations. This mathematical model also observes the rate of case detection and treatment. This article also discusses the analysis of the equilibrium point, the stability of the equilibrium points of the model that has been formed, and the basic reproduction number (R0). This model shows a backward bifurcation, that is the appearance of an endemic equilibrium point when R0<1, which means that the disease will not necessarily disappear even though R0<1. The numerical solution for this model is obtained using the fifth order Runge-Kutta method.