Global properties of a tuberculosis model with lost sight and multi-compartment of latents

A  tuberculosis (TB) model with  lost sight  and multiple latent classes  is considered and studied. We derive the basic reproduction ratio $mathcal R_0$. There is always a globally asymptotically stable equilibrium state. Depending on the value of   $mathcal{R}_0$, this state can be either endemic ($mathcal{R}_0> 1$), or infection-free ($mathcal{R}_0leq 1$). The global asymptotic stability of equilibria is established using Lyapunov functions that combine quadratic, Volterra-type and linear functions. The theory is supported by numerical simulations.