Viral dynamics of HIV-1 with CTL immune response

Wang, Aiping; Li, Michael Y.

doi:10.3934/dcdsb.2020212

Cited by 14 publications

(12 citation statements)

References 43 publications

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“…Numerous differential equation models in the current literature delve into understanding the dynamics of infectious disease spread (e.g. see [1–7]). These models often integrate a recovery component, presuming that infected individuals solely recover due to their immune system, excluding any social factors.…”

Section: Introductionmentioning

confidence: 99%

Modelling the dynamics of product adoption and abandonment

Kong

2024

Proc. R. Soc. A.

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We introduce a new compartmental differential equation model to examine the dynamics of user adoption and abandonment within a product context. This model features a nonlinear adoption rate and encompasses two distinct abandonment dynamics: infectious abandonment stemming from interactions among current and past users, and non-infectious abandonment induced by mass media, advertisements or the emergence of new products. Our exploration encompasses discussions on the existence and stability of model equilibria, as well as the derivation of a critical threshold quantity that regulates the model dynamics. Additionally, we establish criteria for backward and forward bifurcations and various forms of Hopf bifurcation. Detailed scrutiny of an associated optimal control problem is undertaken, starting with the establishment of the existence of an optimal control pair, followed by the determination of the requisite system conditions for this control pair. Extensive numerical simulations are conducted to validate the theoretical findings. Finally, we showcase the model’s efficacy by fitting it to historical data on Facebook’s daily active users, employing the derived parameter values to predict future user counts.

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Section: Introductionmentioning

confidence: 99%

Modelling the dynamics of product adoption and abandonment

Kong

2024

Proc. R. Soc. A.

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“…where T(t) is the concentration of CTLs at time t. The terms σIT, δ T T, and βIT represent, respectively, the rates of stimulation of CTLs, the death of CTLs, and the killing of infected cells by CTLs. The model was revisited in several papers (see, e.g., [11][12][13][14][15][16][17]).…”

Section: Introductionmentioning

confidence: 99%

Global Properties of Cytokine-Enhanced HIV-1 Dynamics Model with Adaptive Immunity and Distributed Delays

Dahy,

Elaiw,

Raezah

et al. 2023

Computation

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In this paper, we study a model that enhances our understanding of cytokine-influenced HIV-1 infection. The impact of adaptive immune response (cytotoxic T lymphocytes (CTLs) and antibodies) and time delay on HIV-1 infection is included. The model takes into account two types of distributional delays, (i) the delay in the HIV-1 infection of CD4+T cells and (ii) the maturation delay of new virions. We first investigated the fundamental characteristics of the system, then found the system’s equilibria. We derived five threshold parameters, ℜi, i = 0, 1,…, 4, which completely determine the existence and stability of the equilibria. The Lyapunov method was used to prove the global asymptotic stability for all equilibria. We illustrate the theoretical results by performing numerical simulations. We also performed a sensitivity analysis on the basic reproduction number ℜ0 and identified the most-sensitive parameters. We found that pyroptosis contributes to the number ℜ0, and then, neglecting it will make ℜ0 underevaluated. Necrosulfonamide and highly active antiretroviral drug therapy (HAART) can be effective in preventing pyroptosis and at reducing viral replication. Further, it was also found that increasing time delays can effectively decrease ℜ0 and, then, inhibit HIV-1 replication. Furthermore, it is shown that both CTLs and antibody immune responses have no effect on ℜ0, while this can result in less HIV-1 infection.

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“…Therefore, De Boer [22] asserted that the bilinear rate cannot represent many immune responses that are working together to manage chronic infection and suggested an immune response function based on a competitive saturation term. Then [23]- [27] opted for the saturated CTL response function.…”

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confidence: 99%

“…Motivated by above biological reasons, in this paper we consider a within-host HIV-1 infection model, the model presented by four fractional order differential equations. The proposed model is a modification for the model presented by Wang et al [23]. The authors in [23] studied the effect of the Cytotoxic T lymphocytes (CTLs) immune response as a saturated term on HIV dynamics when infections being a result of interaction with virus particles but in these study we considered both virus-to-cell and cell-to-cell transmissions.…”

mentioning

confidence: 99%

“…The proposed model is a modification for the model presented by Wang et al [23]. The authors in [23] studied the effect of the Cytotoxic T lymphocytes (CTLs) immune response as a saturated term on HIV dynamics when infections being a result of interaction with virus particles but in these study we considered both virus-to-cell and cell-to-cell transmissions. This manuscript is structured as follows: In Section 2, we provide a definition of fractional-order derivatives and theorems related to them.…”

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confidence: 99%

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Analysis of a fractional order HIV-1 infection model with saturated immune response

Azoz¹,

Hussien²,

Abdelsamea³

2023

Assiut University Journal of Multidisciplinary Scientific Resea

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Human immunodeficiency virus type-1 (HIV-1) is a retrovirus that induces acquired immunodeficiency syndrome (AIDS). HIV-1 targets CD4+ T cells, which are the most numerous white blood cells in the host immune system and play a crucial role in protecting the body from infection. The first case of HIV infection was identified in 1981 and since then HIV has become one of the most deadly infections in the world and has a devastating impact on human health and even life [1]. For a decade, it was thought that the spread of HIV-1 in hosts was primarily due to free circulation of virus particles, with a repeated process consisting of virus attachments to T cells. However recent studies have shown that the infection can also be passed directly from infected cells to susceptible cells.In order to gain a better understanding of virus dynamics within the host and to predict how antiviral treatment effectiveness will affect the course of an infection,

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Viral dynamics of HIV-1 with CTL immune response

Cited by 14 publications

References 43 publications

Modelling the dynamics of product adoption and abandonment

Modelling the dynamics of product adoption and abandonment

Global Properties of Cytokine-Enhanced HIV-1 Dynamics Model with Adaptive Immunity and Distributed Delays

Analysis of a fractional order HIV-1 infection model with saturated immune response

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