A Mathematical Model for the Response of Immune Cells to Mycobacterium Tuberculosis

Abstract

Tuberculosis (TB) is an infectious disease that is a problem almost all over the world. In 2019, the World Health Organization (WHO) reported 10 million new infections each year, with an average of 1.2 million people dying from the dis- ease. Vaccination to healthy people is an effort to protect against infection with this disease. In this paper, a mathematical model of the interaction of the immune response against Mycobacterium tuberculosis with vaccine administration is stu- died. The model is in the form of a system of ordinary differential equations with four variables. Furthermore, an analysis of the stability of the equilibrium point is carried out. The results obtained indicate that the disease-free equilibrium point is globally asymptotically stable if R0 ≤ 1, and unstable if R0 > 1. The sensitivity analysis showed that the infection rate and the bacterial growth rate were the two most influencing factors for the infection’s survival. This study’s results are ex- pected to be reference doctors and paramedics to reduce tuberculosis cases.