scholarly journals Dynamics of an HBV infection model with cell-to-cell transmission and CTL immune response

2019 ◽  
Vol Volume 30 - 2019 - MADEV... ◽  
Author(s):  
Hajar Besbassi ◽  
Zineb Elrhoubari ◽  
Khalid Hattaf ◽  
Yousfi Noura
Keyword(s):  
Chronic Infection ◽  
Hbv Infection ◽  
Infection Model ◽  
Geometrical Approach ◽  
Direct Lyapunov Method ◽  
Cell Infection ◽  
Modes Of Transmission ◽  
Cell Transmission ◽  
Infected Cells ◽  
Disease Free

International audience In this work, we propose a mathematical model to describe the dynamics of the hepatitis B virus (HBV) infection by taking into account the cure of infected cells, the export of precursor cytotoxic T lympho-cytes (CTL) cells from the thymus and both modes of transmission that are the virus-to-cell infection and the cell-to-cell transmission. The local stability of the disease-free equilibrium and the chronic infection equilibrium is obtained via characteristic equations. Furthermore, the global stability of both equilibria is established by using two techniques, the direct Lyapunov method for the disease-free equilibrium and the geometrical approach for the chronic infection equilibrium. Dans ce travail, nous proposons un modèle mathématique pour décrire la dynamique du virus d'hépatite B (HBV) en prenant en compte le taux de guérison de cellules infectées, l'exportation de précurseur cytotoxic des lymphocytes T (CTL) des cellules du thymus et les deux modes de transmission qui sont l'infection virus-à-cellule et la transmission cellule-à-cellule.La stabilité locale de l'équilibre libre et l'équilibre d'infection chronique est obtenue via des équations caractéristiques. En outre, la stabilité globale des deux équilibres est établie en utilisant deux techniques, la méthode directe de Lyapunov pour l'équilibre libre et l'approche géométrique pour l'équilibre d'infection chronique.

scholarly journals Stability Analysis of an Improved HBV Model with CTL Immune Response

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Mostafa Khabouze ◽  
Khalid Hattaf ◽  
Noura Yousfi
Keyword(s):  
Immune Response ◽  
Chronic Infection ◽  
Lyapunov Method ◽  
Geometrical Approach ◽  
Direct Lyapunov Method ◽  
B Virus ◽  
Hbv Model ◽  
Ctl Immune Response ◽  
Disease Free

To better understand the dynamics of the hepatitis B virus (HBV) infection, we introduce an improved HBV model with standard incidence function, cytotoxic T lymphocytes (CTL) immune response, and take into account the effect of the export of precursor CTL cells from the thymus and the role of cytolytic and noncytolytic mechanisms. The local stability of the disease-free equilibrium and the chronic infection equilibrium is obtained via characteristic equations. Furthermore, the global stability of both equilibria is established by using two techniques, the direct Lyapunov method for the disease-free equilibrium and the geometrical approach for the chronic infection equilibrium.

scholarly journals A generalized distributed delay model for HBV infection with two modes of transmission and adaptive immunity: A mathematical study

2021 ◽  
Author(s):  
Kalyan Manna ◽  
khalid hattaf
Keyword(s):  
Adaptive Immunity ◽  
Distributed Delay ◽  
Hbv Infection ◽  
Infection Model ◽  
Delay Model ◽  
Cell Infection ◽  
Modes Of Transmission ◽  
Proposed Model ◽  
Infection Models ◽  
B Virus

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 solu- tions. Five equilibria of the model are identified in terms of five threshold parameters R0, R1, R2, R3 and R4. 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 il- lustrate the applicability of our study. Nonetheless, the results obtained in this study are valid for a wide class of HBV infection models.

scholarly journals Stability and Hopf Bifurcation of a Generalized Chikungunya Virus Infection Model with Two Modes of Transmission and Delays

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Hajar Besbassi ◽  
Khalid Hattaf ◽  
Noura Yousfi
Keyword(s):  
Hopf Bifurcation ◽  
Chikungunya Virus ◽  
Infection Model ◽  
Cell Infection ◽  
Chikv Infection ◽  
Modes Of Transmission ◽  
Functional Methods ◽  
Incidence Functions ◽  
Virus Infection Model ◽  
Disease Free

A generalized chikungunya virus (CHIKV) infection model with nonlinear incidence functions and two time delays is proposed and investigated. The model takes into account both modes of transmission that are virus-to-cell infection and cell-to-cell transmission. Furthermore, the local and global stabilities of the disease-free equilibrium and the chronic infection equilibrium are established by using the linearization and Lyapunov functional methods. Moreover, the existence of Hopf bifurcation is also analyzed. Finally, an application is presented in order to support the analytical results.

Dynamics of a diffusion-driven HBV infection model with capsids and time delay

2017 ◽  
Vol 10 (05) ◽  
pp. 1750062 ◽  
Author(s):  
Kalyan Manna
Keyword(s):  
Steady State ◽  
Time Delay ◽  
Dynamical Behavior ◽  
Hbv Infection ◽  
Infection Model ◽  
Direct Lyapunov Method ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Discrete Time Delay ◽  
Number Formula

In this paper, a diffusive hepatitis B virus (HBV) infection model with a discrete time delay is presented and analyzed, where the spatial mobility of both intracellular capsid covered HBV DNA and HBV and the intracellular delay in the reproduction of infected hepatocytes are taken into account. We define the basic reproduction number [Formula: see text] that determines the dynamical behavior of the model. The local and global stability of the spatially homogeneous steady states are analyzed by using the linearization technique and the direct Lyapunov method, respectively. It is shown that the susceptible uninfected steady state is globally asymptotically stable whenever [Formula: see text] and is unstable whenever [Formula: see text]. Also, the infected steady state is globally asymptotically stable when [Formula: see text]. Finally, numerical simulations are carried out to illustrate the results obtained.

scholarly journals Qualitative Analysis of a Generalized Virus Dynamics Model with Both Modes of Transmission and Distributed Delays

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Khalid Hattaf ◽  
Noura Yousfi
Keyword(s):  
Qualitative Analysis ◽  
Distributed Delays ◽  
Virus Dynamics ◽  
Dynamics Model ◽  
Cell Infection ◽  
Modes Of Transmission ◽  
Proposed Model ◽  
Infection Models ◽  
Infected Cells ◽  
Incidence Functions

We propose a generalized virus dynamics model with distributed delays and both modes of transmission, one by virus-to-cell infection and the other by cell-to-cell transfer. In the proposed model, the distributed delays describe (i) the time needed for infected cells to produce new virions and (ii) the time necessary for the newly produced virions to become mature and infectious. In addition, the infection transmission process is modeled by general incidence functions for both modes. Furthermore, the qualitative analysis of the model is rigorously established and many known viral infection models with discrete and distributed delays are extended and improved.

scholarly journals Accounting for multi-delay effects in an HIV-1 infection model with saturated infection rate, recovery and proliferation of host cells

BIOMATH ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 2012297
Author(s):  
Debadatta Adak ◽  
Nandadulal Bairagi ◽  
Robert Hakl
Keyword(s):  
Infection Rate ◽  
Viral Entry ◽  
Host Cells ◽  
Infection Model ◽  
Multiple Delays ◽  
Delay Effects ◽  
Delayed System ◽  
Infected Cells ◽  
Disease Free ◽  
Hiv 1

Biological models inherently contain delay. Mathematical analysis of a delay-induced model is, however, more difficult compare to its non-delayed counterpart. Difficulties multiply if the model contains multiple delays. In this paper, we analyze a realistic HIV-1 infection model in the presence and absence of multiple delays. We consider self-proliferation of CD4+T cells, nonlinear saturated infection rate and recovery of infected cells due to incomplete reverse transcription in a basic HIV-1 in-host model and incorporate multiple delays to account for successful viral entry and subsequent virus reproduction from the infected cell. Both of delayed and non-delayed system becomes disease-free if the basic reproduction number is less than unity. In the absence of delays, the infected equilibrium is shown to be locally asymptotically stable under some parametric space and unstable otherwise. The system may show unstable oscillatory behaviour in the presence of either delay even when the non-delayed system is stable. The second delay further enhances the instability of the endemic equilibrium which is otherwise stable in the presence of a single delay. Numerical results are shown to be in agreement with the analytical results and reflect quite realistic dynamics observed in HIV-1 infected individuals.

scholarly journals Dynamics of a stochastic HBV infection model with cell-to-cell transmission and immune response

2021 ◽  
Vol 18 (1) ◽  
pp. 616-642
Author(s):  
Xiaoqin Wang ◽  
◽  
Yiping Tan ◽  
Yongli Cai ◽  
Kaifa Wang ◽  
...  
Keyword(s):  
Immune Response ◽  
Hbv Infection ◽  
Infection Model ◽  
Cell Transmission
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