Global dynamics of a latent HIV infection model with general incidence function and multiple delays

Yang, Yu; Dong, Yueping; Takeuchi, Yasuhiro

doi:10.3934/dcdsb.2018207

Cited by 7 publications

(4 citation statements)

References 41 publications

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“…An important reason is that HIV provirus can reside in latently infected CD4 + T-cells, which can live longer and cannot be affected by antiretroviral drugs or immune responses, but can be activated to produce virus by relevant antigens [5]. ereafter, motivated by this factor, many viral infection models with latent cells have been proposed and studied to describe this phenomena [6][7][8][9][10][11][12][13] and references therein. For example, Pankavich [6] proposed and studied the following viral infection model:…”

Section: Introductionmentioning

confidence: 99%

Threshold Dynamics for a Time-Periodic Viral Infection Model with Cell-to-Cell Transmission and Drug Treatments

Huang

2022

Mathematical Problems in Engineering

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In this study, a time-periodic viral infection model incorporating cell-to-cell infection and antiretroviral therapy has been investigated. The basic reproduction number ℛ 0 has been defined as a threshold parameter which governs whether or not the disease dies out. Theoretical results indicate that the disease goes to extinction if ℛ 0 < 1 and otherwise the disease will uniformly persist. The global stabilities of the equilibria for the corresponding autonomous model have been investigated by constructing suitable Lyapunov functions. Moreover, numerical simulations have been carried out to validate the obtained results. The results show that cell-to-cell infection mode may be a barrier to curing the viral infection and increasing the efficacy of protease inhibitors for blocking cell-to-cell infection which will benefit to weaken the severity of the viral infection.

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Section: Introductionmentioning

confidence: 99%

Threshold Dynamics for a Time-Periodic Viral Infection Model with Cell-to-Cell Transmission and Drug Treatments

Huang

2022

Mathematical Problems in Engineering

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“…Based on the above discussion, the consideration of these time delays into the model will reflect much more effective results compared to the model without these time delays. [24][25][26] Recently, most of the clinical studies have been focused on infected patients with elevated aminotransferase levels and circulating hepatitis B "e" antigen (HBeAg). The main idea behind the consideration of the effect of antiviral therapies into the model is because the access to the antiviral therapies becomes regular.…”

Section: Introductionmentioning

confidence: 99%

Stability and bifurcation analysis of hepatitis B‐type virus infection model

Mani

Rakkiyappan

Manivannan

et al. 2021

Math Methods in App Sciences

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The main aim of this study is to analyze the dynamical properties of hepatitis B-type virus (HBV) infection in terms of mathematical model. The presented mathematical model on HBV involves the various factors such as immune impairment, total carrying capacity, logistic growth term, and antiretroviral therapies. In addition, the effect of time delays is also considered into the model, which are inevitable during the activation of immune response and time taken to infect the healthy cells. Mathematically, the qualitative analyses such as stability, bifurcation, and stabilization analysis are performed to explore the dynamical characteristics of HBV over the period of time. The significance of the model parameters is revealed through Hopf-type bifurcation analysis and the global stability analysis of the proposed model. With the help of data set values that are extracted from the literature, the efficiency of the derived theoretical results is explored.

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“…We note that it takes time for the establishment of latent infection, thus another intracellular delay between viral entry and latent infection when viral DNA is integrated into the host cell's DNA, may be indispensable. Although latently infected cells [31,28,27,39,43] and latent infection delay [43,51] have been introduced into the viral models, there are all together few works on the distributed delay induced by latent infection. The current study is devoted to giving an insight into the dynamical behaviors of multiple distributed delays involved in invasion, production and latent infection.…”

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confidence: 99%

“…Motivated by the Refs. [14,34,40,51,9,37], this current paper is concerned with the effects of nonlinear immune response and intracellular distributed delays in the following diffusive HIV-1 model described by…”

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confidence: 99%

Spatiotemporal dynamics for a diffusive HIV-1 infection model with distributed delays and CTL immune response

Liu¹,

Wang²,

Tan³

2022

DCDS-B

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In this study, we develop a diffusive HIV-1 infection model with intracellular invasion, production and latent infection distributed delays, nonlinear incidence rate and nonlinear CTL immune response. The well-posedness, local and global stability for the model proposed are carefully investigated in spite of its strong nonlinearity and high dimension. It is revealed that its threshold dynamics are fully determined by the viral infection reproduction number R 0 and the reproduction number of CTL immune response R 1 . We also observe that the viral load at steady state (SS) fails to decrease even if R 1 increases through unit to lead to a stability switch from immune-inactivated infected SS to immune-activated infected SS. Finally, some simulations are performed to verify the analytical conclusions and we explore the significant impact of delays and CTL immune response on the spatiotemporal dynamics of HIV-1 infection.

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Global dynamics of a latent HIV infection model with general incidence function and multiple delays

Cited by 7 publications

References 41 publications

Threshold Dynamics for a Time-Periodic Viral Infection Model with Cell-to-Cell Transmission and Drug Treatments

Threshold Dynamics for a Time-Periodic Viral Infection Model with Cell-to-Cell Transmission and Drug Treatments

Stability and bifurcation analysis of hepatitis B‐type virus infection model

Spatiotemporal dynamics for a diffusive HIV-1 infection model with distributed delays and CTL immune response

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