Global dynamics of a mathematical model for HTLV-I infection of CD4+ T cells with delayed CTL response

Li, Michael Y.; Shu, Hongying

doi:10.1016/j.nonrwa.2011.02.026

Cited by 110 publications

(56 citation statements)

References 26 publications

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“…These prompt many researchers to study mathematical modelling and model analysis of the interaction between the host cells and viruses such as human immunodeficiency virus (HIV) (see e.g. [3][4][5][6][7]9,15,16,18,22,24]), hepatitis B virus (HBV) [2,12], hepatitis C virus (HCV) [14,20,21], human T cell leukemia [11] and dengue virus [23], etc. There are many benefits from mathematical models of viral infection including: (i) they provide important quantitative insights into viral dynamics in vivo, (ii) they can improve diagnosis and treatment strategies which raise hopes of patients infected with viruses, (iii) they can be used to estimate key parameter values that control the infection process.…”

Section: Introductionmentioning

confidence: 99%

Global stability analysis of humoral immunity virus dynamics model including latently infected cells

Ełaiw

2015

Journal of Biological Dynamics

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In this paper, we propose and analyse a virus dynamics model with humoral immune response including latently infected cells. The incidence rate is given by Beddington-DeAngelis functional response. We have derived two threshold parameters, the basic infection reproduction number R 0 and the humoral immune response activation number R 1 which completely determined the basic and global properties of the virus dynamics model. By constructing suitable Lyapunov functions and applying LaSalle's invariance principle we have proven that if R 0 ≤ 1, then the infection-free equilibrium is globally asymptotically stable (GAS), if R 1 ≤ 1 < R 0 , then the chronic-infection equilibrium without humoral immune response is GAS, and if R 1 > 1, then the chronic-infection equilibrium with humoral immune response is globally asymptotically stable. These results are further illustrated by numerical simulations.

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Section: Introductionmentioning

confidence: 99%

Global stability analysis of humoral immunity virus dynamics model including latently infected cells

Ełaiw

2015

Journal of Biological Dynamics

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“…In the literature, CTL immune response has been incorporated into mathematical models of different pathogen infections (see e.g. [18,24,25,27,32,33,37,38,48]). The function φ(y, x) has been chosen in different forms such as: (i) constant, φ(y, x) = c 1 [31]; (ii) linear, φ(y, x) = ρy [1,23,44]; (iii) nonlinear φ(y, x) = c 2 yx (see e.g [27,30]).…”

Section: Introductionmentioning

confidence: 99%

Stability of pathogen dynamics models with viral and cellular infections and immune impairment

Ełaiw¹,

Raezah²,

Alofi³

2018

J. Nonlinear Sci. Appl.

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We study the global stability analysis of pathogen infection models with immune impairment. Both pathogen-to-susceptible and infected-to-susceptible transmissions have been considered. We drive the basic reproduction parameter R 0 , which determines the global dynamics of models. Using the method of Lyapunov function, we established the global stability of the steady states of the models. Numerical simulations are used to confirm the theoretical results.

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“…Refs. [28][29][30][31][32][33][34][35][36][37][38][39]. The basic viral pathogen infection model with CTL immune response has been presented in Ref.…”

Section: Introductionmentioning

confidence: 99%

Stability of CTL immunity pathogen dynamics model with capsids and distributed delay

2017

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In this paper, a pathogen dynamics model with capsids and saturated incidence has been proposed and analyzed. Cytotoxic T Lymphocyte (CTL) immune response and two distributed time delays have been incorporated into the model. The nonnegativity and boundedness of the solutions of the proposed model have been shown. Two threshold parameters which fully determine the existence and stability of the three steady states of the model have been computed. Using the method of Lyapunov function, the global stability of the steady states of the model has been established. The theoretical results have been confirmed by numerical simulations.

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Global dynamics of a mathematical model for HTLV-I infection of CD4+ T cells with delayed CTL response

Cited by 110 publications

References 26 publications

Global stability analysis of humoral immunity virus dynamics model including latently infected cells

Global stability analysis of humoral immunity virus dynamics model including latently infected cells

Stability of pathogen dynamics models with viral and cellular infections and immune impairment

Stability of CTL immunity pathogen dynamics model with capsids and distributed delay

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