Global stability properties for a delayed virus dynamics model with humoral immunity response and absorption effect

Abstract

A model for virus infection with absorption effect and humoral immunity response consisting of system of delay differential equations has been investigated. By direct calculations, the basic number of reproduction and humoral immune-activated reproduction numbers which are also known as threshold values have been obtained. The equilibria of the proposed model, the infection free equilibrium, humoral immune-inactivated equilibrium and humoral immune-activated equilibrium which are completely based on the basic number of reproduction, and humoral immune-activated reproduction number have been found by directly solving the system. Results obtained for Lyapunov functionals and using LaSalle's invariance principle with sufficient conditions, are: (i) the infection free equilibrium satisfied the global asymptotic stability criteria if the basic reproduction number is below unity or equal to unity. (ii) the humoral immune-inactivated equilibrium is globally asymptotically stable, provided that the humoral immune-activated reproduction number is below unit or equal to unity and the basic reproduction number exceeds unity, and (iii) the humoral immune-activated equilibrium satisfies the global asymptotic stability criteria for the case when humoral immune-activated reproduction number exceeds unity.