title: Asymptotic behavior of HIV-1 epidemic model with infinite distributed intracellular delays.
abstract: In this study, asymptotic analysis of an HIV-1 epidemic model with distributed intracellular delays is proposed. One delay term represents the latent period which is the time when the target cells are contacted by the virus particles and the time the contacted cells become actively infected and the second delay term represents the virus production period which is the time when the new virions are created within the cell and are released from the cell. The infection free equilibrium and the chronic-infection equilibrium have been shown to be locally asymptotically stable by using Rouths Hurwiths criterion and general theory of delay differential equations. Similarly, by using Lyapunov functionals and LaSalle's invariance principle, it is proved that if the basic reproduction ratio is less than unity, then the infection-free equilibrium is globally asymptotically stable, and if the basic reproduction ratio is greater than unity, the chronic-infection equilibrium is globally asymptotically stable. Finally, numerical results with conclusion are discussed.
authors.affiliation: Department of Mathematics, University of Malakand, Chakdara Dir (Lower), Khyber Pakhtunkhawa Pakistan.
authors.forename: Nigar
authors.initials: N
authors.lastname: Ali
authors.affiliation: Department of Mathematics, University of Malakand, Chakdara Dir (Lower), Khyber Pakhtunkhawa Pakistan.
authors.forename: Gul
authors.initials: G
authors.lastname: Zaman
keywords: Distributed delay; HIV-1 epidemic model; Stability analysis; Unique positive solution