Modelling effects of treatment at home on tuberculosis transmission dynamics

A tuberculosis model with two kinds of treatment, that is, treatment at home and treatment in hospital, is constructed. Mathematical analyses show that the dynamics of model are determined by the basic reproduction number R0. If R0 < 1, then the disease free equilibrium is globally asymptotically stable. If R0 > 1, the endemic equilibrium is globally asymptotically stable when patients who are not cured do not transfer from hospital to home. Numerical simulations are also given to support our theoretical results. Our results show that the treatment at home has great negative influence on the spread of the tuberculosis.