Global Stability of a Tuberculosis Model with Chemoprophylaxis for Latent Infection

A tuberculosis model which incorporates chemo prophylaxis for latent infection and treatment for infectious infection is presented. The epidemic threshold known as the reproduction number is given, and the dynamics of the model is determined by the basic reproductive number. All solutions converge to the disease-free equilibrium when the basic reproduction number is less than or equal to one. When the basic reproduction number exceeds one, the model has a unique endemic equilibrium, which is globally stable. At last, to control the spread of tuberculosis, effects of chemo prophylaxis for latent tuberculosis infection are simulated and discussed, and the results show that chemo prophylaxis will do better in controlling the number of infective due to reducing the transfer rate of the latent progression to active tuberculosis.