Analysis of stability and Hopf bifurcation for HIV-1 dynamics with PI and three intracellular delays

Monica, C.; Pitchaimani, M.

doi:10.1016/j.nonrwa.2015.07.014

Cited by 40 publications

(17 citation statements)

References 44 publications

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“…In this subsection, we establish the existence of the steady states of the model in Equations (19)- (23). The basic reproduction number of the system in Equations (19)-(23) is defined as:…”

Section: Steady Statesmentioning

confidence: 99%

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Global Stability of Within-Host Virus Dynamics Models with Multitarget Cells

2018

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In this paper, we study the stability analysis of two within-host virus dynamics models with antibody immune response. We assume that the virus infects n classes of target cells. The second model considers two types of infected cells: (i) latently infected cells; and (ii) actively infected cells that produce the virus particles. For each model, we derive a biological threshold number R 0. Using the method of Lyapunov function, we establish the global stability of the steady states of the models. The theoretical results are confirmed by numerical simulations.

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“…In this subsection, we establish the existence of the steady states of the model in Equations (19)- (23). The basic reproduction number of the system in Equations (19)-(23) is defined as:…”

Section: Steady Statesmentioning

confidence: 99%

“…To illustrate our theoretical results, we perform numerical simulations for the systems in Equations (9)- (12) and Equations (19)- (23). We consider the case n = 2.…”

Section: Numerical Simulationsmentioning

confidence: 99%

Global Stability of Within-Host Virus Dynamics Models with Multitarget Cells

2018

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“…Over the recent years, several researchers have used mathematical models to explore the dynamics of various human pathogen infections. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] Mathematical models and their analysis are helpful to enlighten the dynamical behavior of pathogens. Moreover, these models provide helpful suggestions for clinical treatment.…”

Section: Introductionmentioning

confidence: 99%

Stability of an adaptive immunity pathogen dynamics model with latency and multiple delays

Ełaiw

AlShamrani

2018

Math Methods in App Sciences

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We incorporate three distributed time delays into the model of pathogen dynamics with antibody and Cytotoxic T Lymphocyte (CTL) immune responses. We consider both actively and latently infected cells. The pathogen-target incidence rate, production/proliferation, and removal rates of the cells and pathogens are represented by general nonlinear functions. We show that the solutions of the proposed model are nonnegative and ultimately bounded. We derive four threshold parameters that fully determine the existence and stability of the five steady states of the model. Using Lyapunov functionals, we established the global stability of the steady states of the model. The theoretical results are confirmed by numerical simulations. KEYWORDS adaptive immune response, global stability, intracellular delay, Lyapunov function, pathogen infection Math Meth Appl Sci. 2018;41:6645-6672.wileyonlinelibrary.com/journal/mma

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“…The basic model may not describe the nonlinear virus dynamics during the infection stages [18]. Therefore, several works have been done to modify the basic model by considering different factors such as: immune response, [10,33], nonlinear forms of the incidence rate [1,12,17,18,34,39], nonlinear production/removal rate of compartments [10,15,18], latently infected cells [2,6], intracellular time delay [8,9,19,22,23,28,33]. Georgescu and Hsieh [15] have generalized the above model by including the latent infected cells and representing the incidence rate, the production and death rate of all compartments by general nonlinear functions as:Ṫ = f(T ) − h(V)g(T ),…”

Section: Introductionmentioning

confidence: 99%

Stability of general virus dynamics models with both cellular and viral infections

Ełaiw¹,

Raezah²,

Shehata³

2017

J. Nonlinear Sci. Appl.

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We consider two general models for the virus dynamics with virus-to-target and infected-to-target infections. We assume that the virus-target and infected-target incidences, the production and clearance rates of all compartments are modeled by general nonlinear functions which satisfy a set of reasonable conditions. We incorporate the latently infected cells in the second model. For each model we prove the existence of the equilibria and calculate the basic reproduction number R 0 . We use suitable Lyapunov functions and apply LaSalle's invariance principle to prove the global asymptotic stability of the all equilibria of the models. We confirm the theoretical results by numerical simulations.

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Analysis of stability and Hopf bifurcation for HIV-1 dynamics with PI and three intracellular delays

Cited by 40 publications

References 44 publications

Global Stability of Within-Host Virus Dynamics Models with Multitarget Cells

Global Stability of Within-Host Virus Dynamics Models with Multitarget Cells

Stability of an adaptive immunity pathogen dynamics model with latency and multiple delays

Stability of general virus dynamics models with both cellular and viral infections

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