A Hepatitis B and C Virus Model with Age since Infection that Exhibits Backward Bifurcation

Qesmi, Redouane; ElSaadany, Susie; Heffernan, Jane M.; Wu, Jianhong

doi:10.1137/10079690x

Cited by 38 publications

(26 citation statements)

References 28 publications

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“…These prompt many researchers to study mathematical modelling and model analysis of the interaction between the host cells and viruses such as human immunodeficiency virus (HIV) (see e.g. [3][4][5][6][7]9,15,16,18,22,24]), hepatitis B virus (HBV) [2,12], hepatitis C virus (HCV) [14,20,21], human T cell leukemia [11] and dengue virus [23], etc. There are many benefits from mathematical models of viral infection including: (i) they provide important quantitative insights into viral dynamics in vivo, (ii) they can improve diagnosis and treatment strategies which raise hopes of patients infected with viruses, (iii) they can be used to estimate key parameter values that control the infection process.…”

Section: Introductionmentioning

confidence: 99%

Global stability analysis of humoral immunity virus dynamics model including latently infected cells

Ełaiw

2015

Journal of Biological Dynamics

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In this paper, we propose and analyse a virus dynamics model with humoral immune response including latently infected cells. The incidence rate is given by Beddington-DeAngelis functional response. We have derived two threshold parameters, the basic infection reproduction number R 0 and the humoral immune response activation number R 1 which completely determined the basic and global properties of the virus dynamics model. By constructing suitable Lyapunov functions and applying LaSalle's invariance principle we have proven that if R 0 ≤ 1, then the infection-free equilibrium is globally asymptotically stable (GAS), if R 1 ≤ 1 < R 0 , then the chronic-infection equilibrium without humoral immune response is GAS, and if R 1 > 1, then the chronic-infection equilibrium with humoral immune response is globally asymptotically stable. These results are further illustrated by numerical simulations.

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Section: Introductionmentioning

confidence: 99%

Global stability analysis of humoral immunity virus dynamics model including latently infected cells

Ełaiw

2015

Journal of Biological Dynamics

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“…Various mathematical models of within-host virus dynamics, based on the interactions between pathogens and individual host, have presented a significant role in understanding the mechanisms of virus infections over the past two decades (for example, [1][2][3][4][5][6][7][8][9][10]). Because age structure is an important factor in the modeling of infectious diseases, there have been many age-structured mathematical models describing the dynamics of virus infection in vivo [11][12][13][14][15][16][17][18]. These age-structured models can be used to explain human immunodeficiency virus (HIV) infection [11,12,14,16], hepatitis B virus infection [15], hepatitis C virus infection [17], hepatitis C virus and hepatitis B infection [18], and other virus infections.…”

Section: Introductionmentioning

confidence: 99%

“…Because age structure is an important factor in the modeling of infectious diseases, there have been many age-structured mathematical models describing the dynamics of virus infection in vivo [11][12][13][14][15][16][17][18]. These age-structured models can be used to explain human immunodeficiency virus (HIV) infection [11,12,14,16], hepatitis B virus infection [15], hepatitis C virus infection [17], hepatitis C virus and hepatitis B infection [18], and other virus infections. Most of the age-structured virus dynamics models assume that there exists an age that is defined as the time that has passed since the infection of the cell.…”

Section: Introductionmentioning

confidence: 99%

Global dynamics of an age‐structured virus model with saturation effects

Duan

Yuan

2016

Math Methods in App Sciences

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An infection‐age virus dynamics model for human immunodeficiency virus (or hepatitis B virus) infections with saturation effects of infection rate and immune response is investigated in this paper. It is shown that the global dynamics of the model is completely determined by two critical values R0, the basic reproductive number for viral infection, and R1, the viral reproductive number at the immune‐free infection steady state (R11 > R1, the immune‐free infected steady state E∗ is globally asymptotically stable; while if R1>1, the antibody immune infected steady state falseÊ is globally asymptotically stable. Moreover, our results show that ignoring the saturation effects of antibody immune response or infection rate will result in an overestimate of the antibody immune reproductive number. Copyright © 2016 John Wiley & Sons, Ltd.

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“…Several works have been devoted to propose and analyze mathematical models of viral infectious dynamics such as human immunodeficiency virus (HIV) [1][2][3][4][5][6][7][8][9][10][11][12][13][14], hepatitis B virus (HBV) [15][16][17][18][19][20], hepatitis C virus (HCV) [21][22][23] and human T cell leukemia (HTLV) [24], etc. Mathematical models of viral infection can help for understanding the viral dynamics and developing antiviral drug therapies.…”

Section: Introductionmentioning

confidence: 99%

Global Properties of General Viral Infection Models with Humoral Immune Response

Ełaiw

AlShamrani

2015

Differ Equ Dyn Syst

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In this paper, we study the global properties of two general models for viral infection with humoral immune response. The incidence rate of infection, the removal rate of infected cells, the production and neutralize rates of viruses and the activation and removal rates of B cells are given by more general nonlinear functions. The second model generalizes the first one by taking into account the latently infected cells. We assume that the latent-toactive conversion rate is also given by a more general nonlinear function. For both models, we derive two threshold parameters and establish a set of conditions on the general functions which are sufficient to determine the global dynamics of the models. By using suitable Lyapunov functions and LaSalle's invariance principle, we prove the global asymptotic stability of all equilibria of the models.

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A Hepatitis B and C Virus Model with Age since Infection that Exhibits Backward Bifurcation

Cited by 38 publications

References 28 publications

Global stability analysis of humoral immunity virus dynamics model including latently infected cells

Global stability analysis of humoral immunity virus dynamics model including latently infected cells

Global dynamics of an age‐structured virus model with saturation effects

Global Properties of General Viral Infection Models with Humoral Immune Response

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