Dynamical analysis of tuberculosis disease with SVEIR model

Abstract

In this article, we propose a tuberculosis model with drug-sensitive (DS-TB) and multidrug-resistant (MDR-TB). The population is divided into 6 sub-population, namely susceptible (S), vaccinated (V), latent (E), active DS-TB (I_s), active MDR-TB (I_r), and recovered (R). There are two equilibrium points, i.e. disease-free equilibrium (DFE) point and endemic equilibrium (EE) point. The basic reproduction number (R₀) is determined by using the next generation matrix method. It can be shown that the DFE point is locally and globally asymptotically stable when R₀<1. Meanwhile, the EE point is exist if R₀>1 and locally asymptotically stable when it holds Routh-Hurwitz criterion. The numerical simulation is conducted to illustrate the analysis results.