Dynamics of a generalized viral infection model with adaptive immune response

Hattaf, Khalid; Khabouze, Mostafa; Yousfi, Noura

doi:10.1007/s40435-014-0130-5

Cited by 18 publications

(16 citation statements)

References 16 publications

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“…Whereas, when this basic reproduction number is greater than one, the activation of one or both arms of adaptive immune response is unable to eradicate the virus and the viral infection persists, but plays an important role in the reduction the viral load, increasing the healthy cells and decreasing the infected cells. This conclusion was observed by Hattaf et al [2]. The last biological conclusion of this work is to give two possible reasons of non-coordination between the humoral and cellular immune responses that could be the explanation of the dysfunction of the adaptive immune response in viral infections such HBV, which is still largely incomplete [32].…”

Section: Discussionsupporting

confidence: 63%

“…Using the same method to find the equilibria of model [2], we obtain the following result. (1) has an infection equilibrium with only cellular immune response…”

Section: Theorem 21 For Every Initial Conditionsmentioning

confidence: 99%

“…This general function includes several types of incidence rate existing in the literature. All the parameters given in model (1) are positive constants and the general incidence function f (x, y, v) is continuously differentiable in the interior of IR 3 + and satisfies the three fundamental hypotheses given in [1] and used in [2][3][4][5][6][7][8], that are:…”

Section: Introductionmentioning

confidence: 99%

“…The state variables and all parameters of model (2) have the same biological meanings as those in (1). On the other hand, if we choose g 1 …”

Section: Introductionmentioning

confidence: 99%

“…Also, the model of Su et al [25] is a particular case of [23] when τ 1 = τ 2 = 0. In addition, when τ 1 = τ 2 = 0, we obtain the generalized viral infection model with adaptive immune response proposed by Hattaf et al in [2].…”

Section: Introductionmentioning

confidence: 99%

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A class of delayed viral infection models with general incidence rate and adaptive immune response

Hattaf

Yousfi

2015

Int. J. Dynam. Control

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To model the role of the adaptive immune response in viral infection, take account the time needed for infected cells to produce new virions after viral entry and the time necessary for the newly produced virions to become mature and infectious, we propose three generalized models that describe the interactions between virus, host cells, antibodies and cytotoxic T lymphocytes (CTL) cells. The incidence rate of the infection into three models is given by a general function which includes many special cases and depends on the uninfected cells, infected cells and virus. Our main results show that the global dynamics of the three models under certain hypotheses on the incidence function is fully determined by five threshold parameters called the reproduction numbers for viral infection, for antibody immune response, for CTL immune response, for antibody immune competition and for CTL immune competition. Several viral infection models with discrete, finite and infinite distributed delays existing in other previous studies are extended and generalized. Furthermore, we give some biological findings of our analytical results.

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Section: Discussionsupporting

confidence: 63%

“…Using the same method to find the equilibria of model [2], we obtain the following result. (1) has an infection equilibrium with only cellular immune response…”

Section: Theorem 21 For Every Initial Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…The state variables and all parameters of model (2) have the same biological meanings as those in (1). On the other hand, if we choose g 1 …”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A class of delayed viral infection models with general incidence rate and adaptive immune response

Hattaf

Yousfi

2015

Int. J. Dynam. Control

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SARS‐CoV‐2 and influenza viruses: Strategies to cope with coinfection and bioinformatics perspective

Ghaznavi

Shirvaliloo

Sargazi

et al. 2022

Cell Biology International

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Almost a century after the devastating pandemic of the Spanish flu, humankind is facing the relatively comparable global outbreak of COVID‐19. COVID‐19 is an infectious disease caused by SARS‐CoV‐2 with an unprecedented transmission pattern. In the face of the recent repercussions of COVID‐19, many have argued that the clinical experience with influenza through the last century may have tremendous implications in the containment of this newly emerged viral disease. During the last 2 years, from the emergence of COVID‐19, tremendous advances have been made in diagnosing and treating coinfections. Several approved vaccines are available now for the primary prevention of COVID‐19 and specific treatments exist to alleviate symptoms. The present review article aims to discuss the pathophysiology, diagnosis, and treatment of SARS‐CoV‐2 and influenza A virus coinfection while delivering a bioinformatics‐based insight into this subject matter.

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A generalized distributed delay model for hepatitis B virus infection with two modes of transmission and adaptive immunity: A mathematical study

Manna

Hattaf²

2022

Math Methods in App Sciences

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In this paper, we formulate a generalized hepatitis B virus (HBV) infection model with two modes of infection transmission and adaptive immunity and investigate its dynamical properties. Both the virus‐to‐cell and cell‐to‐cell infection transmissions are modeled by general functions which satisfy some biologically motivated assumptions. Furthermore, the model incorporates three distributed time delays for the production of active infected hepatocytes, mature capsids, and virions. The well‐posedness of the proposed model is established by showing the non‐negativity and boundedness of solutions. Five equilibria of the model are identified in terms of five threshold parameters R0,0.1emR1,0.1emR2,0.1emR3$$ {R}_0,{R}_1,{R}_2,{R}_3 $$, and R4$$ {R}_4 $$. Further, the global stability analysis of each equilibrium under certain conditions is carried out by employing suitable Lyapunov function and LaSalle's invariance principle. Finally, we present an example with numerical simulations to illustrate the applicability of our study. Nonetheless, the results obtained in this study are valid for a wide class of HBV infection models.

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Dynamics of a generalized viral infection model with adaptive immune response

Cited by 18 publications

References 16 publications

A class of delayed viral infection models with general incidence rate and adaptive immune response

A class of delayed viral infection models with general incidence rate and adaptive immune response

SARS‐CoV‐2 and influenza viruses: Strategies to cope with coinfection and bioinformatics perspective

A generalized distributed delay model for hepatitis B virus infection with two modes of transmission and adaptive immunity: A mathematical study

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