Dynamics of a Class of HIV Infection Models with Cure of Infected Cells in Eclipse Stage

Maziane, Mehdi; Lotfi, El Mehdi; Hattaf, Khalid; Yousfi, Noura

doi:10.1007/s10441-015-9263-y

Cited by 22 publications

(20 citation statements)

References 38 publications

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“…Example 2: an HIV cellular model. We consider the HIV infection model with cure rate of infected cells in eclipse stage as proposed by Maziane et al [42]. This model contains also four variables: the uninfected CD4 + T cells (T ), infected cells in the eclipse stage (unproductive cells, denoted by E), productive infected cells (I), and free virus particles (V ).…”

Section: Applicationsmentioning

confidence: 99%

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Lyapunov functions for fractional-order systems in biology: Methods and applications

Boukhouima

Hattaf

Lotfi

et al. 2020

Chaos, Solitons & Fractals

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We prove new estimates of the Caputo derivative of order α ∈ (0, 1] for some specific functions. The estimations are shown useful to construct Lyapunov functions for systems of fractional differential equations in biology, based on those known for ordinary differential equations, and therefore useful to determine the global stability of the equilibrium points for fractional systems. To illustrate the usefulness of our theoretical results, a fractional HIV population model and a fractional cellular model are studied. More precisely, we construct suitable Lyapunov functionals to demonstrate the global stability of the free and endemic equilibriums, for both fractional models, and we also perform some numerical simulations that confirm our choices.

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Section: Applicationsmentioning

confidence: 99%

“…which is the average number of secondary infections produced by one productive infected cell during the period of infection when all cells are uninfected. Moreover, Maziane et al [42] show that model (17) is globally asymptotically stable. The proof is done by using the following Lyapunov function in R 4 + :…”

Section: Applicationsmentioning

confidence: 99%

Lyapunov functions for fractional-order systems in biology: Methods and applications

Boukhouima

Hattaf

Lotfi

et al. 2020

Chaos, Solitons & Fractals

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“…For the Beddington-DeAngelis incidence function βS 1 + α 1 S + α 2 I [1,3,7], see Figure 5. For the specific non-linear incidence function βS 1 + α 1 S + α 2 I + α 3 SI [10,11,14,21,25], see Figure 6. In Tables 3 and 4, we compute the basic reproduction number R 0 for each incidence function proposed in Table 1 with the parameter values from Table 2.…”

Section: Numerical Simulations: Application To Moroccan Hiv/aids Datamentioning

confidence: 99%

A Minimal HIV-AIDS Infection Model with General Incidence Rate and Application to Morocco Data

Lotfi

Mahrouf

Maziane

et al. 2019

Stat., optim. inf. comput.

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We study the global dynamics of a SICA infection model with general incidence rate. The proposed model is calibrated with cumulative cases of infection by HIV-AIDS in Morocco from 1986 to 2015. We first prove that our model is biologically and mathematically well-posed. Stability analysis of different steady states is performed and threshold parameters are identified where the model exhibits clearance of infection or maintenance of a chronic infection. Furthermore, we examine the robustness of the model to some parameter values by examining the sensitivity of the basic reproduction number. Finally, using numerical simulations with real data from Morocco, we show that the model predicts well such reality.

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“…In 2014, Hu et al [4] replaced the bilinear incidence rate in [3] by a saturated infection rate and they studied the global stability of equilibria. In 2015, Maziane et al [5] improved the model of [4] by considering the Hattaf 's incidence rate [6] that includes the common types such as the bilinear incidence rate, the saturated incidence rate, the Beddington-DeAngelis functional response [7,8] and the Crowley-Martin functional response [9].…”

Section: Introductionmentioning

confidence: 99%

Spatiotemporal Dynamics of an HIV Infection Model with Delay in Immune Response Activation

Maziane

Hattaf

Yousfi

2018

International Journal of Differential Equations

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We propose and analyse an human immunodeficiency virus (HIV) infection model with spatial diffusion and delay in the immune response activation. In the proposed model, the immune response is presented by the cytotoxic T lymphocytes (CTL) cells. We first prove that the model is well-posed by showing the global existence, positivity, and boundedness of solutions. The model has three equilibria, namely, the free-infection equilibrium, the immune-free infection equilibrium, and the chronic infection equilibrium. The global stability of the first two equilibria is fully characterized by two threshold parameters that are the basic reproduction number R0 and the CTL immune response reproduction number R1. The stability of the last equilibrium depends on R0 and R1 as well as time delay τ in the CTL activation. We prove that the chronic infection equilibrium is locally asymptotically stable when the time delay is sufficiently small, while it loses its stability and a Hopf bifurcation occurs when τ passes through a certain critical value.

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Dynamics of a Class of HIV Infection Models with Cure of Infected Cells in Eclipse Stage

Cited by 22 publications

References 38 publications

Lyapunov functions for fractional-order systems in biology: Methods and applications

Lyapunov functions for fractional-order systems in biology: Methods and applications

A Minimal HIV-AIDS Infection Model with General Incidence Rate and Application to Morocco Data

Spatiotemporal Dynamics of an HIV Infection Model with Delay in Immune Response Activation

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