A Fractional Order Model for Viral Infection with Cure of Infected Cells and Humoral Immunity

Boukhouima, Adnane; Hattaf, Khalid; Yousfi, Noura

doi:10.1155/2018/1019242

Cited by 6 publications

(5 citation statements)

References 42 publications

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“…Let u(t) = (T (t), E(t), I(t), V (t)) be a solution of ( 19)- (20). According to our Corollary 2, since L given by ( 18) is a Lyapunov function for the ordinary differential equations (17) of the form described by (12), then L is also a Lyapunov function for the fractional-order system ( 19)-(20).…”

Section: A(t)mentioning

confidence: 94%

“…Corollary 2. If L is a Lyapunov function for the ordinary differential equation (1) of the form described by (12), then L is also a Lyapunov function for the Caputo fractional-order system (5).…”

Section: Description Of the Methodsmentioning

confidence: 99%

“…They observe, via numerical simulations, that when the derivative order is near to one, then the Caputo-Fabrizio non-integer order derivative reveals better absorbing characteristics. For other related works, see, e.g., [4,12,16,36,40,45,58].…”

Section: Introductionmentioning

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: A(t)mentioning

confidence: 94%

Section: Description Of the Methodsmentioning

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

Self Cite

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show abstract

“…Therefore, the use of general incidence function allows to give a general and more real vision of the viral infection spread. Several works use this kind of general incidence function [33][34][35][36]. Motivated by previous works, the objective of the present work is to generalize the previous models.…”

Section: Introductionmentioning

confidence: 99%

A generalized fractional hepatitis B virus infection modelwith both cell-to-cell and virus-to-cell transmissions

Yaagoub,

Sadki,

Allali

2024

Preprint

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In this paper, we suggest a generalized fractional hepatitis B viral infection model with twomodes of transmission that are cell-to-cell and virus-to-cell. These two modes of transmissionwill be represented by two generalized incidence functions. We take into account the humanbody adaptive immunity, that is represented by antibody and cytotoxic T-lymphocyte immuneresponses. We begin the study of this model by giving some theorems concerning the existence,positivity and boundness of the model solutions. We have shown that the model has a free-disease equilibrium point and other four endemic steady states. We give the relationship betweenthe existence of these steady states and their corresponding reproductive numbers. By usingthe Lyapunov method and LaSalle's invariance principle, we have shown the different theoremsof global stability to the problem steady states. Some numerical simulations are presented inorder to confirm our theoretical fndings about the stability of steady states and to show the effectiveness of fractional derivative order on the stability of all equilibria. We observe that thechoice of generalized incidence functions can provide a clearer understanding of the stability of equilibria and can incorporate a wide range of classical incidence functions. Finally, good infectiontreatment helps considerably to irradiate the infection.

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“…Boukhouima et al [12,13] studied the dynamics of virus in the human body through a fractional derivative. Hattaf [14] developed the new generalized fractional derivative and applied it to the analysis of HIV dynamics in the body.…”

Section: Introductionmentioning

confidence: 99%

Fractional Derivative Model for Analysis of HIV and Malaria Transmission Dynamics

Cheneke

2023

Discrete Dynamics in Nature and Society

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In this study, a Caputo fractional derivative is employed to develop a model of malaria and HIV transmission dynamics with optimal control. Also, the model’s basic properties are shown, and the basic reproduction number is computed using the next-generation matrix method. Additionally, the order of fractional derivative analysis shows that the infected group decreases at the beginning for the higher-order of fractional derivative. Moreover, the early activation of memory effects through public health education reduces the impact of malaria and HIV infections on further progression and transmission. On the other hand, effective optimal controls reduce the occurrence and prevalence of HIV and malaria infections from the beginning to the end of the investigation. Finally, the numerical simulations are done for the justification of analytical solutions with numerical solutions of the model. Moreover, the MATLAB platform is incorporated for numerical simulation of the solutions.

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A Fractional Order Model for Viral Infection with Cure of Infected Cells and Humoral Immunity

Cited by 6 publications

References 42 publications

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

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

A generalized fractional hepatitis B virus infection modelwith both cell-to-cell and virus-to-cell transmissions

Fractional Derivative Model for Analysis of HIV and Malaria Transmission Dynamics

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