Local Stability Analysis of an Infection-Age Mathematical Model for Tuberculosis Disease Dynamics

Abstract

An infection age structured mathematical model for tuberculosis disease dynamics is investigated in this paper. The infectious population is structured according to time and age of infection. An explicit formula for the basic reproductive number, R0 of the model is obtained. We showed that the disease-free equilibrium (DFE) state is locally asymptotically stable if R0 < 1 and unstable if otherwise. This simply means that tuberculosis could be controlled in a population when the basic reproduction number is less than unity. Keywords: Basic reproduction number; Infection-age; Local Stability; Tuberculosis

Keywords

• Basic reproduction number
• Infection-age
• Local Stability
• Tuberculosis