Analysis of a viral infection model with immune impairment, intracellular delay and general non-linear incidence rate

Ávila-Vales, Eric; Chan-Chí, Noé; García-Almeida, Gerardo E.

doi:10.1016/j.chaos.2014.08.009

Cited by 10 publications

(11 citation statements)

References 17 publications

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“…The model with special distribution. The general distribution function in model (3) allows us to include two special forms of intracellular delays existing in the literature, including the Dirac delta function and Gamma distribution, seeing [1,5,22,25,26,36]. We first consider the generic delay kernel of the Dirac's form h(r) = δ(r−τ ) for τ ≥ 0.…”

Section: 1mentioning

confidence: 99%

“…In the case of τ ≥ 0 and τ 1 = 0, when the basic reproduction number R 0 > 1 the global attractivity for the chronicinfected equilibrium E * (x * , y * , z * ) of model (1) was achieved using two different Lyapunov functionals by [26] and [36], respectively. Moreover, Wang et al [36] established the local stability and globally asymptotical stability of E * of the model (1) under the conditions that R 0 > 1 and…”

mentioning

confidence: 99%

“…And the same parameters in 3with (1) have the same meanings, and the biological meanings of the remaining parameters are also described in the lower part of Table 1. The general distribution function considered here allows us to include several special forms of intracellular delays existing in the literatures (e.g., [1,5,22,25,26,36]). More specifically, when the distribution h(r) = δ(r − τ ) is a delta function on τ ≥ 0, where δ(•) stands for the Dirac delta function, model (3) becomes a DDE system with a discrete delay for τ > 0, and for τ = 0 it reduces to the DDE model (1) studied in [26,36] if α 1 = α 2 = ω = m = 0 and σ = 1.…”

mentioning

confidence: 99%

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Complete dynamical analysis for a nonlinear HTLV-I infection model with distributed delay, CTL response and immune impairment

Wang¹,

Liu²,

Li³

et al. 2020

Discrete &Amp; Continuous Dynamical Systems - B

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It is well known that CTL (cytotoxic T lymphocyte) immune response could be broadly classified into lytic and nonlytic components, nonlinear functions can better reproduce saturated effects in the interaction processes between cell and viral populations, and distributed intracellular delay can realistically reflect the stochastic element in the delay effects. For these reasons, we develop an HTLV-I (Human T-cell leukemia virus type I) infection model with nonlinear lytic and nonlytic CTL immune responses, nonlinear incidence rate, distributed intracellular delay and immune impairment. Through conducting complete analysis, it is revealed that all these factors influence the concentration level of infected T-cells at the chronic-infection equilibrium, whereas intracellular distributed delay and nonlinear incidence rate may change the expression of the basic reproduction number R 0 in the context where the model proposed still preserves the threshold dynamics. Our analysis results obtained may improve several existing works by comparison. We also perform global sensitivity analysis for R 0 in order to explore the effective strategies of lowering the concentration level of infected T-cells.

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Section: 1mentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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Complete dynamical analysis for a nonlinear HTLV-I infection model with distributed delay, CTL response and immune impairment

Wang¹,

Liu²,

Li³

et al. 2020

Discrete &Amp; Continuous Dynamical Systems - B

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“…Pathogen infection models with immune impairment have been studied in several works (see e.g. [2,17,19,20,35,43]). …”

Section: Introductionmentioning

confidence: 99%

“…The works presented in [2,17,19,20,35,43] assume that the susceptible cells become infected due to pathogen contacts. However, pathogen can also spread by direct infected-to-susceptible transmission.…”

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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Mathematical Study of a Fractional-Order General Pathogen Dynamic Model with Immune Impairment

Azoz

Hussien

2021

Studies in Systems, Decision and Control

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Analysis of a viral infection model with immune impairment, intracellular delay and general non-linear incidence rate

Cited by 10 publications

References 17 publications

Complete dynamical analysis for a nonlinear HTLV-I infection model with distributed delay, CTL response and immune impairment

Complete dynamical analysis for a nonlinear HTLV-I infection model with distributed delay, CTL response and immune impairment

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

Mathematical Study of a Fractional-Order General Pathogen Dynamic Model with Immune Impairment

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