Analysis of HIV models with two time delays

Alshorman, Areej; Wang, Xia; Meyer, M. Joseph; Liang, Rong

doi:10.1080/17513758.2016.1148202

Cited by 39 publications

(50 citation statements)

References 55 publications

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“…Model (6)- (11) assumes that, once the HIV contacts a CD4 + T cell, it becomes infected in the same time. Neglecting the time delays is an unrealistic assumption (see, e.g., [29,30]). The aim of this paper is to propose HIV infection models which improve model (6)-(11) by taking into account three time delays, discrete or distributed.…”

Section: U(t) = (1 -ε 1 )λ 3 χ S(t) P(t) -β 4 G 3 U(t) mentioning

confidence: 99%

Effect of cellular reservoirs and delays on the global dynamics of HIV

2018

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We investigate general HIV infection models with three types of infected cells: latently infected cells, long-lived productively infected cells, and short-lived productively infected cells. We incorporate three discrete or distributed time delays into the models. Moreover, we consider the effect of humoral immunity on the dynamical behavior of the HIV. The HIV-target incidence rate, production/proliferation, and removal rates of the cells and HIV are represented by general nonlinear functions. We show that the solutions of the proposed model are nonnegative and ultimately bounded. We derive two threshold parameters which fully determine the existence and stability of the three steady states of the model. Using Lyapunov functionals, we establish the global stability of the steady states of the model. The theoretical results are confirmed by numerical simulations.MSC: 34D20; 34D23; 37N25; 92B05

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Section: U(t) = (1 -ε 1 )λ 3 χ S(t) P(t) -β 4 G 3 U(t) mentioning

confidence: 99%

Effect of cellular reservoirs and delays on the global dynamics of HIV

2018

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“…Parameter values were chosen from several modelling papers [2,39,[42][43][44]. They were either based on experimental data or chosen to generate the dynamics of the virus and latently infected cells that agree with the current knowledge of HIV infection and treatment.…”

Section: Numerical Illustration Of Stability Resultsmentioning

confidence: 99%

“…Next, we prove the boundedness of the solution of system (1) with the initial condition (2). From the positivity of the solution and the first equation of (1), we obtain…”

Section: Theorem 21: Let (T(t) L(t) I(t) V(t)) Be a Solution Of Smentioning

confidence: 99%

“…It is clear that τ 1 < τ 2 according to the viral life cycle. As assumed in HIV latent infection models [2,34,43,44], a very small fraction of CD4 + T cell infection leads to HIV latency. They don't produce new virus unless activated by antigens.…”

Section: Model Formulationmentioning

confidence: 99%

“…Latently infected CD4 + T cells live long, are not affected by antiretroviral drugs or immune responses, but can be activated to produce virus by relevant antigens. In the present paper, on the basis of the models by Lai and Zou [24,25] and Alshorman et al [2], we developed an HIV latent infection model incorporating both the cell-free virus infection and cell-to-cell transmission. Two delays, one the time between viral entry and viral DNA integration into the host cell's DNA and the other the time between viral entry and viral production, have also been included in the model.…”

Section: Contactmentioning

confidence: 99%

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Mathematical analysis of an HIV latent infection model including both virus-to-cell infection and cell-to-cell transmission

Wang

Tang

Song

et al. 2016

Journal of Biological Dynamics

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HIV can infect cells via virus-to-cell infection or cell-to-cell viral transmission. These two infection modes may occur in a synergistic way and facilitate viral spread within an infected individual. In this paper, we developed an HIV latent infection model including both modes of transmission and time delays between viral entry and integration or viral production. We analysed the model by defining the basic reproductive number, showing the existence, positivity and boundedness of the solution, and proving the local and global stability of the infection-free and infected steady states. Numerical simulations have been performed to illustrate the theoretical results and evaluate the effects of time delays and fractions of infection leading to latency on the virus dynamics. The estimates of the relative contributions to the HIV latent reservoir and the virus population from the two modes of transmission have also been provided.

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Global behavior and optimal control of a dengue transmission model with standard incidence rates and self‐protection

Guo,

Pan,

Cui

et al. 2024

Math Methods in App Sciences

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It takes into account that conscious, susceptible individuals with self‐protection cannot be infected by mosquito bites, a seven‐dimensional dengue transmission model with self‐protection, and two different standard incidence rates are proposed. Our focus is on discussing the global behavior and the optimal control of the model. We first calculate the control reproduction number and determine that if , the model has a unique dengue equilibrium . Furthermore, we obtain the local stability of dengue‐free equilibrium and the dengue equilibrium by using the method of proof by contradiction. By utilizing the limit system of the model and the Lyapunov direct method, we acquire that is globally stable if ; is globally attractive if , and if , the model is weakly persistent with a thorough analysis, and then is globally stable. Finally, in order to minimize investment in dengue transmission, an optimal control strategy with four control variables is presented using Pontryagin's minimum principle.

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Analysis of HIV models with two time delays

Cited by 39 publications

References 55 publications

Effect of cellular reservoirs and delays on the global dynamics of HIV

Effect of cellular reservoirs and delays on the global dynamics of HIV

Mathematical analysis of an HIV latent infection model including both virus-to-cell infection and cell-to-cell transmission

Global behavior and optimal control of a dengue transmission model with standard incidence rates and self‐protection

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