MATHEMATICAL MODEL of Mycobacterium tuberculosis INFECTION in the LUNG - Prasojo Widianto, Wisnu
Tuberculosis (TB) is a contagious disease and is one of the highest causes of death in the world. Tuberculosis is divided into two types, latent TB infection and active TB disease. Tuberculosis is caused by a bacterial infection of Mycobacterium tuberculosis (Mtb) in the lungs. This bacteria attack macrophage cells and have the ability to live and replicate inside the cells. Mtb bacteria can live in the lungs without causing any clinical symptoms on infected person. In this final project, we modeled the immune response against Mtb bacterial infection in the lungs. This model is a five-dimensional differential equation system that represents change in the number of healthy, infected, activated macrophage cells, extracellular bacterial particles, and naive T cells. Model analysis proves the existence of two equilibrium points, disease free equilibrium and endemic equilibrium that represent latent or active tuberculosis based on the number of bacteria. Bifurcation analysis shows that if the replication of the Mtb bacterial (????) is large enough, the immune system can’t completely eliminate bacterial infection so the Mtb bacteria will continue to replicate in the lungs.