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

Document Type: Research Paper

Authors

1 Laboratory of Mathematics, Department of Mathematics and Computer Science, Faculty of Science, University of Douala, PO Box 24157 Douala, Cameroon. UMI 209 IRD & UPMC UMMISCO, Bondy, France Project team GRIMCAPE-Cameroon

2 Department of Mathematics, Faculty of Science, University of Yaounde I, PO Box 812 Yaounde, Cameroon

3 Laboratory of Mathematics, Department of Mathematics and Computer Science, Faculty of Science, University of Douala, PO Box 24157 Douala, Cameroon. UMI 209 IRD & UPMC UMMISCO, Bondy, France Project team GRIMCAPE-Cameroon

Abstract

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 ($\mathcal{R}_0\leq 1$). 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.

Keywords