Global dynamics of discrete mathematical models of tuberculosis

Abstract

In this paper, we develop discrete models of Tuberculosis (TB). This includes SEI endogenous and exogenous models without treatment. These models are then extended to a SEIT model with treatment. We develop two types of net reproduction numbers, one is the traditional (Formula presented.) which is based on the disease-free equilibrium, and a new net reproduction number (Formula presented.) based on the endemic equilibrium. It is shown that the disease-free equilibrium is globally asymptotically stable if (Formula presented.) and unstable if (Formula presented.). Moreover, the endemic equilibrium is locally asymptotically stable if (Formula presented.).