Stability analysis of HIV-1 model with multiple delays

Nigar Ali,Obaid Algahtani,Gul Zaman

doi:10.1186/s13662-016-0808-4

Nigar Ali, Obaid Algahtani + Show 1 more

Open Access

https://doi.org/10.1186/s13662-016-0808-4

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Abstract

A mathematical model for HIV-1 infection with multiple delays is proposed. These delays account for (i) the delay in contact process between the uninfected cells virus, (ii) a latent period between the time target cells which are contacted by the virus particles and the time the virions enter the cells, and (iii) a virus production period for new virions to be produced within and released from the infected cells. For this model, the basic reproductive number is identified and its threshold property is discussed. The uninfected and infected steady states are shown to be locally as well as globally asymptotically stable. The value of the basic reproductive number shows that increasing any one of these delays will decrease this number. This may suggest a new direction for new drugs that can prolong the infection process and spreading of virus. The proved results have potential applications in HIV-1 therapy.

Highlights

Mathematical modeling in epidemiology provides understanding of the mechanisms that influence the spread of a disease and suggests control strategies
The HIV infection is characterized by three different phases, namely, the primary infection, a clinically asymptomatic stage, and acquired immunodeficiency syndrome (AIDS)
Clinical research combined with mathematical modeling has enhanced progress in the understanding of the HIV- infection [ ]

Summary

Introduction

Mathematical modeling in epidemiology provides understanding of the mechanisms that influence the spread of a disease and suggests control strategies. The novelty of the proposed model is that it considers a delay in the process of infection of healthy T cells, and in virus production. It will be shown that an infection-free equilibrium, E , is locally as well as globally asymptotically stable. Stability of the disease-free equilibrium E0 we show the dynamical behavior of the system ( ) at E .

Results

Conclusion