Analysis of mathematical models describing the immune response of <i>Mycobacterium tuberculosis</i>

This paper studies the dynamic behavior of a class of microkinetic models of Mycobacterium tuberculosis (Mtb). This model can help us understand how the numbers of bacteria and immune cells change during infection, including initial recruitment and subsequent proliferation. The basic reproduction number and the threshold theory of the model are obtained through calculation and analysis, and there exists sterile equilibrium and bacterial equilibrium, and they are globally stable under different conditions. In addition, sensitivity analyses help to determine which parameters have the most important impact on Mtb invasion of the host. Numerical simulations can reflect the different stages of infection associated with the clearance, survival, or growth and multiplication of Mtb, where the effectiveness of the immune system determines whether the infection can be controlled, kept in a latent state, or allowed to progress to active tuberculosis with visible symptoms.