Mathematical analysis of a tuberculosis model with differential infectivity

This paper deals with the global properties of a tuberculosis model with mass action incidence and two differential infectivity. The direct Lyapunov method enables us to prove that the considered model is globally stable: There is always a globally asymptotically stable equilibrium state. Depending on the value of the basic reproduction number R 0 , this state can be either endemic ( R 0 > 1 ), or infection-free ( R 0 ⩽ 1 ). Numerical results are provided to illustrate analytical results.