Global analysis for an HIV infection model with CTL immune response and infected cells in eclipse phase

Karam Allali; Jaouad Danane; Yang Kuang

doi:10.3390/app7080861

Global analysis for an HIV infection model with CTL immune response and infected cells in eclipse phase

Karam Allali, Jaouad Danane, Yang Kuang

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18 Scopus citations

Abstract

A modified mathematical model describing the human immunodeficiency virus (HIV) pathogenesis with cytotoxic T-lymphocytes (CTL) and infected cells in eclipse phase is presented and studied in this paper. The model under consideration also includes a saturated rate describing viral infection. First, the positivity and boundedness of solutions for nonnegative initial data are proved. Next, the global stability of the disease free steady state and the endemic steady states are established depending on the basic reproduction number R₀ and the CTL immune response reproduction number R_CTL . Moreover, numerical simulations are performed in order to show the numerical stability for each steady state and to support our theoretical findings. Our model based findings suggest that system immunity represented by CTL may control viral replication and reduce the infection.

Original language	English (US)
Article number	861
Journal	Applied Sciences (Switzerland)
Volume	7
Issue number	8
DOIs	https://doi.org/10.3390/app7080861
State	Published - Aug 21 2017

Keywords

CTL immune response
Global stability
HIV infection model
Viral dynamics

ASJC Scopus subject areas

Materials Science(all)
Instrumentation
Engineering(all)
Process Chemistry and Technology
Computer Science Applications
Fluid Flow and Transfer Processes

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title = "Global analysis for an HIV infection model with CTL immune response and infected cells in eclipse phase",

abstract = "A modified mathematical model describing the human immunodeficiency virus (HIV) pathogenesis with cytotoxic T-lymphocytes (CTL) and infected cells in eclipse phase is presented and studied in this paper. The model under consideration also includes a saturated rate describing viral infection. First, the positivity and boundedness of solutions for nonnegative initial data are proved. Next, the global stability of the disease free steady state and the endemic steady states are established depending on the basic reproduction number R0 and the CTL immune response reproduction number RCTL . Moreover, numerical simulations are performed in order to show the numerical stability for each steady state and to support our theoretical findings. Our model based findings suggest that system immunity represented by CTL may control viral replication and reduce the infection.",

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T1 - Global analysis for an HIV infection model with CTL immune response and infected cells in eclipse phase

AU - Allali, Karam

AU - Danane, Jaouad

AU - Kuang, Yang

PY - 2017/8/21

Y1 - 2017/8/21

N2 - A modified mathematical model describing the human immunodeficiency virus (HIV) pathogenesis with cytotoxic T-lymphocytes (CTL) and infected cells in eclipse phase is presented and studied in this paper. The model under consideration also includes a saturated rate describing viral infection. First, the positivity and boundedness of solutions for nonnegative initial data are proved. Next, the global stability of the disease free steady state and the endemic steady states are established depending on the basic reproduction number R0 and the CTL immune response reproduction number RCTL . Moreover, numerical simulations are performed in order to show the numerical stability for each steady state and to support our theoretical findings. Our model based findings suggest that system immunity represented by CTL may control viral replication and reduce the infection.

AB - A modified mathematical model describing the human immunodeficiency virus (HIV) pathogenesis with cytotoxic T-lymphocytes (CTL) and infected cells in eclipse phase is presented and studied in this paper. The model under consideration also includes a saturated rate describing viral infection. First, the positivity and boundedness of solutions for nonnegative initial data are proved. Next, the global stability of the disease free steady state and the endemic steady states are established depending on the basic reproduction number R0 and the CTL immune response reproduction number RCTL . Moreover, numerical simulations are performed in order to show the numerical stability for each steady state and to support our theoretical findings. Our model based findings suggest that system immunity represented by CTL may control viral replication and reduce the infection.

KW - CTL immune response

KW - Global stability

KW - HIV infection model

KW - Viral dynamics

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Global analysis for an HIV infection model with CTL immune response and infected cells in eclipse phase

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Keywords

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