Mathematical analysis of a virus dynamics model with general incidence rate and cure rate

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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“…The following theorems investigate the global stability of the steady states of system (12)- (17). Let us define the function…”

Section: Global Propertiesmentioning

confidence: 99%

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

2018

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“…If we substitute u * 1 and u * 2 in the systems (2) and (11), we obtain the following optimality system:…”

Section: Isrn Biomathematicsmentioning

confidence: 99%

“…Next, we define the state and adjoint variables x(t), y(t), v(t), z(t), λ 1 (t), λ 2 (t), λ 3 (t), λ 4 (t) and the controls u 1 (t), u 2 Now a combination of forward and backward difference approximation, we obtain Algorithm 1.…”

Section: Numerical Simulationsmentioning

confidence: 99%

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Optimal Control of a Delayed HIV Infection Model with Immune Response Using an Efficient Numerical Method

Hattaf

Yousfi

2012

ISRN Biomathematics

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We present a delay-differential equation model with optimal control that describes the interactions between human immunodeficiency virus (HIV), CD4 + T cells, and cell-mediated immune response. Both the treatment and the intracellular delay are incorporated into the model in order to improve therapies to cure HIV infection. The optimal controls represent the efficiency of drug treatment in inhibiting viral production and preventing new infections. Existence for the optimal control pair is established, Pontryagin's maximum principle is used to characterize these optimal controls, and the optimality system is derived. For the numerical simulation, we propose a new algorithm based on the forward and backward difference approximation.

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“…On the other hand, in the literature of epidemiology, it has increasingly been asserted that the incidence rate, characterizing the rate of newly infected cells, should be written by not bilinear but general nonlinear functions (see, e.g., [8,9,26]). We point out that since both the model (1.1) does not consider cell-mediated cytotoxic T lymphocytes (CTLs) immune response and model (1.2) does not incorporate non-separable incidence rate, in this paper, we combine these two considerations to formulate our model.…”

Section: Introductionmentioning

confidence: 99%

Impact of non-separable incidence rates on global dynamics of virus model with cell-mediated, humoral immune responses

Enatsu¹,

Wang²,

Kuniya³

2017

J. Nonlinear Sci. Appl.

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In this paper, we study the dynamical behavior of a virus model into which cell-mediated and humoral immune responses are incorporated. The global stability of an infection-free equilibrium and four infected equilibria is established via a Lyapunov functional approach. The present construction methods are applicable to a wide range of incidence rates that are monotone increasing with respect to concentration of uninfected cells and concave with respect to the concentration of free virus particles. In addition, when the incidence rate is monotone increasing with respect to concentration of free virus particles, the functional approach plays an important role in determining the global stability of each of the four infected equilibria. This implies that the dynamical behavior of virus prevalence would be determined by basic reproduction numbers when the "saturation effect" for free virus particles appears. We point out that the incidence rate includes not only separable incidence rate but also non-separable incidence rate such as standard incidence and Beddington-DeAngelis functional response.

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Mathematical analysis of a virus dynamics model with general incidence rate and cure rate

Cited by 122 publications

References 24 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

Optimal Control of a Delayed HIV Infection Model with Immune Response Using an Efficient Numerical Method

Impact of non-separable incidence rates on global dynamics of virus model with cell-mediated, humoral immune responses

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