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: see text] which is based on the disease-free equilibrium, and a new net reproduction number [Formula: see text] based on the endemic equilibrium. It is shown that the disease-free equilibrium is globally asymptotically stable if [Formula: see text] and unstable if [Formula: see text]. Moreover, the endemic equilibrium is locally asymptotically stable if [Formula: see text].

Keywords

• Tuberculosis
• treatment
• disease-free
• endemic
• endogenous
• exogenous