Modelling the Adaptive Immune Response in HBV Infection Model with HBV DNA-Containing Capsids

Harroudi, Sanaa; Meskaf, Adil; Allali, Karam

doi:10.1007/s12591-020-00549-1

Cited by 5 publications

(6 citation statements)

References 21 publications

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“…The models including the role of the adaptive immunity in fighting the free virions and reducing the infected hepatocytes were investigated in Harroudi et al. ( 2020 ), Jiang and Wang ( 2014 ), Yousf et al. ( 2011 ).…”

Section: Introductionmentioning

confidence: 99%

Dynamical analysis of a general delayed HBV infection model with capsids and adaptive immune response in presence of exposed infected hepatocytes

Foko

2024

J. Math. Biol.

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The aim of this paper is to develop and investigate a novel mathematical model of the dynamical behaviors of chronic hepatitis B virus infection. The model includes exposed infected hepatocytes, intracellular HBV DNA-containing capsids, uses a general incidence function for viral infection covering a variety of special cases available in the literature, and describes the interaction of cytotoxic T lymphocytes that kill the infected hepatocytes and the magnitude of B-cells that send antibody immune defense to neutralize free virions. Further, one time delay is incorporated to account for actual capsids production. The other time delays are used to account for maturation of capsids and free viruses. We start with the analysis of the proposed model by establishing the local and global existence, uniqueness, non-negativity and boundedness of solutions. After defined the threshold parameters, we discuss the stability properties of all possible steady state constants by using the crafty Lyapunov functionals, the LaSalle’s invariance principle and linearization methods. The impacts of the three time delays on the HBV infection transmission are discussed through local and global sensitivity analysis of the basic reproduction number and of the classes of infected states. Finally, an application is provided and numerical simulations are performed to illustrate and interpret the theoretical results obtained. It is suggested that, a good strategy to eradicate or to control HBV infection within a host should concentrate on any drugs that may prolong the values of the three delays.

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Section: Introductionmentioning

confidence: 99%

Dynamical analysis of a general delayed HBV infection model with capsids and adaptive immune response in presence of exposed infected hepatocytes

Foko

2024

J. Math. Biol.

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“…Some models include HBV treatment through drug therapy, e.g., the work of Lewin et al [43] and Yosyingyong and Viriyapong [62], whereas some models include an adaptive immune response, e.g., the work of Yousfi et al [64], Chenari et al [13] and Manna et al [49]. Further, some researchers have also included HBV DNA-containing capsids in their models, e.g., the papers by Manna et al [46][47][48][49] and Harroudi et al [28]. In addition, some researchers have included time delays in their model.…”

Section: Introductionmentioning

confidence: 99%

Optimal control of a multiple delay model for hepatitis B virus infection of hepatocytes with DNA-containing capsids, immune response and drug therapy

Yosyingyong,

Viriyapong,

Moore

2024

J. Math. Computer Sci.

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Since the number of patients with chronic hepatitis B virus (HBV) infection is still high globally, appropriate strategies for therapy control are required. In this study, we propose an HBV model consisting of six populations, namely uninfected hepatocytes, infected hepatocytes, HBV DNA-containing-capsids, free viruses, antibodies and cytotoxic T-lymphocytes. The model also includes an adaptive immune response, cure rate of infected hepatocytes, two time delays and two control therapies. The two time delays are delay of virus production after infection by HBV and delay of antigenic stimulation generating cytotoxic T-lymphocytes. The two optimal controls are a therapy for blocking new infection and a therapy for inhibiting viral production. The existence, uniqueness, non-negativity and boundedness of model solutions are first proved. The model is shown to have three equilibrium states, namely infection-free, immune-free and endemic. The basic reproduction number for the stability of the infection-free equilibrium is derived and a sensitivity analysis is carried out to determine the most important parameters to change to control the disease. Then optimal control and the Pontryagin maximum principle are used to maximize the concentrations of uninfected hepatocytes, antibodies and cytotoxic T-lymphocytes at minimum cost.

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“…To date, no mathematical models have been presented to consider viral dynamics with these biological factors (CTL immune responses, reaction‐diffusion, two infection modes, nonlinear incidence, two intracellular delays) all together. For example, reaction‐diffusion, delay, and cell‐to‐cell transmission are not considered in the model 19 . The host immune system plays an important role in the progress of the viral infection.…”

Section: Introductionmentioning

confidence: 99%

“…[13][14][15][16] Studies have indicated that CD4 + cytotoxic T lymphocytes (CTLs) can potentially participate in the immune clearance of infected hepatocytes. 17,18 In their work, 19 Harroudi et al studied an HBV infection model with HBV DNA-containing capsids and the adaptive immune response by using a system of six ordinary differential equations. Recently, an susceptible-infected-recovered (SIR) compartmental mathematical model of HBV was investigated by introducing a nonlinear saturated incidence rate and then being solved by continuous Galerkin Petrov and Runge Kutta method in Mehmood et al 20 Li et al 21 established an HBV model with random interference infection rate by incorporating drug sensitive virus and drug resistant virus.…”

Section: Introductionmentioning

confidence: 99%

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A delayed diffusive HBV model with nonlinear incidence and CTL immune response

Zhang

Wang

2022

Math Methods in App Sciences

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In this paper, we develop a diffusive and delayed hepatitis B virus (HBV) infection model, which incorporates both virus-to-cell and cell-to-cell transmissions along with cytotoxic T lymphocyte (CTL) immune response. Two threshold parameters ℜ 0 (basic reproduction number) and ℜ 1 (immune response reproduction number) are defined, which determine the dynamic behavior of the model. Employing the approach of Lyapunov functionals, we show that the infection-free steady state is globally asymptotically stable when ℜ 0 ≤ 1; the immune-free infected steady state is globally asymptotically stable when ℜ 1 ≤ 1 < ℜ 0 ; and the immune-present steady state is globally asymptotically stable when ℜ 0 > 1, ℜ 1 > 1, and 𝜑(I) = I. We perform the sensitivity and uncertainly analysis on ℜ 0 with respect to parameters and find that the most important parameter that drives the HBV infection is the mortality of HBV DNA capsids. Moreover, the theoretical results are supported with numerical simulations.

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Modelling the Adaptive Immune Response in HBV Infection Model with HBV DNA-Containing Capsids

Cited by 5 publications

References 21 publications

Dynamical analysis of a general delayed HBV infection model with capsids and adaptive immune response in presence of exposed infected hepatocytes

Dynamical analysis of a general delayed HBV infection model with capsids and adaptive immune response in presence of exposed infected hepatocytes

Optimal control of a multiple delay model for hepatitis B virus infection of hepatocytes with DNA-containing capsids, immune response and drug therapy

A delayed diffusive HBV model with nonlinear incidence and CTL immune response

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