Mathematical Model for the Growth of Mycobacterium Tuberculosis Infection in the Lungs: - Dewanti, Retno Wahyu; Widianto, Wisnu Prasojo; Apri, Mochamad; Nuraini, Nuning; Fakhruddin, Muhammad (The Indonesian Bio-Mathematical Society, 2025)
In this work, we develop a population dynamics model of Mycobacterium tuberculosis (Mtb), the bacteria responsible for tuberculosis (TB), to evaluate the impact of bacterial competition on infection prevalence. We consider two types of Mtb population growth: The first is caused by bacteria that grow inside each infected macrophage and is believed to be correlated with the number of infected macrophages; The second is that extracellular bacteria grow through self-replication. In this study, we modeled the immune response to Mtb bacterial infection in the lungs using a five-dimensional differential equation system. This model represents changes in the number of healthy macrophages, infected macrophages, activated macrophages cells, extracellular bacterial particles, and naive T cells. Qualitative analysis and numerical results reveal the existence of two equilibrium points: disease-free equilibrium and endemic equilibrium, which represent latent or active tuberculosis based on the number of bacteria. In addition, a sensitive analysis of the model parameters shows that macrophages are not sufficient to control the initial invasion of Mtb. The immune system must therefore employ more complex defense mechanisms to contain Mtb infection, such as recruiting various elements of immune system and forming granulomas.