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 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.

Analysis of the Granularity of Task Decomposition in Enterprise Alliance Based on System Dynamics

2011 ◽  
Vol 314-316 ◽  
pp. 487-491
Author(s):  
Xian Zhang
Keyword(s):  
Qualitative Analysis ◽  
System Dynamics ◽  
System Dynamics Model ◽  
Key Factors ◽  
Dynamics Model ◽  
Task Decomposition ◽  
Proposed Model ◽  
Product Manufacturing ◽  
Manufacturing Time ◽  
Dynamics Method

The influence brought by the granularity of task decomposition on the key factors of enterprise aliance was studied based on system dynamics method. These factors includs inter-restriction, product manufacturing time, collaboration fee, Alliance leader benefit, capability and compatibility. Causality diagram and system dynamics model were established for these factors. This paper also developed a simulation program for the granularity of task decomposition based on the system dynamics model and validated the effectiveness of the proposed model by a qualitative analysis. The results show that it is a workable method to research the granularity of task decomposition in enterprise aliance using system dynamics theory.

GLOBAL STABILITY OF A GENERAL VIRUS DYNAMICS MODEL WITH MULTI-STAGED INFECTED PROGRESSION AND HUMORAL IMMUNITY

2016 ◽  
Vol 24 (04) ◽  
pp. 535-560 ◽  
Author(s):  
A. M. ELAIW ◽  
N. H. ALSHAMRANI
Keyword(s):  
Humoral Immunity ◽  
Lyapunov Functions ◽  
Dynamical Behavior ◽  
Target Cells ◽  
Global Dynamics ◽  
Virus Dynamics ◽  
Nonlinear Functions ◽  
Dynamics Model ◽  
Number Formula ◽  
Infected Cells

In this paper, we propose an [Formula: see text]-dimensional nonlinear virus dynamics model that describes the interactions of the virus, uninfected target cells, [Formula: see text]-stages of infected cells and B cells. We assume that the incidence rate of infection, the generation and removal rates of all compartments are given by general nonlinear functions. We derive two threshold parameters, the basic reproduction number, [Formula: see text] and the humoral immunity number, [Formula: see text] and establish a set of conditions on the general functions which are sufficient to determine the global dynamics of the model. Utilizing Lyapunov functions and LaSalle’s invariance principle, the global asymptotic stability of all steady states of the model is proved. Numerical simulations are conducted for specific forms of the general functions in order to illustrate the dynamical behavior.

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.

scholarly journals Spatiotemporal Dynamics of a Generalized Viral Infection Model with Distributed Delays and CTL Immune Response

Computation ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 21 ◽  
Author(s):  
Khalid Hattaf
Keyword(s):  
Immune Response ◽  
Viral Infection ◽  
Cytotoxic T Lymphocyte ◽  
Distributed Delays ◽  
Infection Model ◽  
Cell Infection ◽  
Incidence Functions ◽  
Dynamics Models ◽  
Ctl Immune Response ◽  
Viral Infection Model

In this paper, we propose and investigate a diffusive viral infection model with distributed delays and cytotoxic T lymphocyte (CTL) immune response. Also, both routes of infection that are virus-to-cell infection and cell-to-cell transmission are modeled by two general nonlinear incidence functions. The well-posedness of the proposed model is also proved by establishing the global existence, uniqueness, nonnegativity and boundedness of solutions. Moreover, the threshold parameters and the global asymptotic stability of equilibria are obtained. Furthermore, diffusive and delayed virus dynamics models presented in many previous studies are improved and generalized.

Impact of adaptive immune response and cellular infection on delayed virus dynamics with multi-stages of infected cells

2019 ◽  
Vol 13 (01) ◽  
pp. 2050003
Author(s):  
A. M. Elaiw ◽  
N. H. AlShamrani
Keyword(s):  
Immune Response ◽  
Immune Responses ◽  
Time Delays ◽  
Adaptive Immune Response ◽  
Virus Dynamics ◽  
Nonlinear Functions ◽  
Dynamics Model ◽  
Adaptive Immune ◽  
Infected Cells ◽  
Theoretical Results

In this investigation, we propose and analyze a virus dynamics model with multi-stages of infected cells. The model incorporates the effect of both humoral and cell-mediated immune responses. We consider two modes of transmissions, virus-to-cell and cell-to-cell. Multiple intracellular discrete-time delays have been integrated into the model. The incidence rate of infection as well as the generation and removal rates of all compartments are described by general nonlinear functions. We derive five threshold parameters which determine the existence of the equilibria of the model under consideration. A set of conditions on the general functions has been established which is sufficient to investigate the global stability of the five equilibria of the model. The global asymptotic stability of all equilibria is proven by utilizing Lyapunov function and LaSalle’s invariance principle. The theoretical results are illustrated by numerical simulations of the model with specific forms of the general functions.

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.

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