Stability of a Two-Strain Tuberculosis Model with General Contact Rate

Abstract

A two-strain tuberculosis model with general contact rate which allows tuberculosis patients with the drug-sensitive Mycobacterium tuberculosis strain to be treated is presented. The model includes both drug-sensitive and drug-resistant strains. A detailed qualitative analysis about positivity, boundedness, existence, uniqueness and global stability of the equilibria of this model is carried out. Analytical results of the model show that the quantities $R_1$ and $R_2$, which represent the basic reproduction numbers of the sensitive and resistant strains, respectively, provide the threshold conditions which determine the competitive outcomes of the two strains. Numerical simulations are also conducted to confirm and extend the analytic results.