Global stability in a competitive infection-age structured model

Abstract

We study a competitive infection-age structured SI model between two diseases. The wellposedness of the system is handled by using integrated semigroups theory, while the existence and the stability of disease-free or endemic equilibria are ensured, depending on the basic reproduction number R x 0 and R y 0 of each strain. We then exhibit Lyapunov functionals to analyse the global stability and we prove that the disease-free equilibrium is globally asymptotically stable whenever max{R x 0 , R y 0 } ≤ 1. With respect to explicit basin of attraction, the competitive exclusion principle occurs in the case where R x 0 = R y 0 and max{R x 0 , R y 0 } > 1, meaning that the strain with the largest R0 persists and eliminates the other strain. In the limit case R x 0 = R 0 y > 1, an infinite number of endemic equilibria exists and constitute a globally attractive set.Mathematics Subject Classification. 35B35, 35B40, 47D62, 92D30.The dates will be set by the publisher.

Threshold dynamics of time-delay in HIV infection model with immune impairment

“…In literature, studies have focused on stability and bifurcation analysis in which the corresponding conditions have been introduced. For more details, refer to [2,19,14,20,24]. The stability and bifurcation of an optimally controlled HIV model with delays were investigated in [31].…”