On the interactions of sensitive and resistant Mycobacterium tuberculosis to antibiotics

•We model the interaction among macrophages, T cells and Mtb into the granuloma.•The results shows the existence of granulomas with or without sensitive bacteria.•Qualitative analysis reveals the existence of forward and backward bifurcations.•It is established conditions that determine the latency state or active TB.

In this work we propose a system of non linear ordinary differential equations for the dynamics of Mycobacterium tuberculosis (Mtb) within the host, in order to study the role of macrophages, T cells and antibiotics in the control of sensitive and resistant Mtb. Conditions for the persistence of sensitive and resistant bacteria are given in terms of the secondary infections produced by bacteria and macrophages, the immune response, and the antibiotic treatment. Model analysis predicts backward bifurcations for certain values of the parameters. In this case, the dynamics is characterized by the coexistence of two infection states with low and high bacteria load, respectively.