scholarly journals Global Dynamics of an Hepatitis C Virus Mathematical Cellular Model with a Logistic Term

2019 ◽  
Vol 12 (3) ◽  
pp. 944-959
Author(s):  
Alexis Nangue ◽  
Thiery Donfack ◽  
David Avava Ndode Yafago
Keyword(s):  
Mathematical Model ◽  
Hepatitis C Virus ◽  
Hepatitis C ◽  
Lyapunov Function ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Cellular Model ◽  
Free Virus ◽  
Globally Asymptotically Stable ◽  
Initial Values

In this paper, the aim is to analyze the global dynamics of Hepatitis C Virus (HCV) cellular mathematical model under therapy with uninfected hepatocytes proliferation. We prove that the solution of the model with positive initial values are global, positive and bounded. In addition, firstly we show that the model is locally asymptotically stable at free virus equilibrium and also at infected equilibrium. Secondly we show that the model is globally asymptotically stable at the free virus equilibrium by using an appropriate lyapunov function.

scholarly journals Global Dynamics of an SIQR Model with Vaccination and Elimination Hybrid Strategies

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 328 ◽  
Author(s):  
Yanli Ma ◽  
Jia-Bao Liu ◽  
Haixia Li
Keyword(s):  
Lyapunov Function ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Disease Free ◽  
The Basic Reproduction Number

In this paper, an SIQR (Susceptible, Infected, Quarantined, Recovered) epidemic model with vaccination, elimination, and quarantine hybrid strategies is proposed, and the dynamics of this model are analyzed by both theoretical and numerical means. Firstly, the basic reproduction number R 0 , which determines whether the disease is extinct or not, is derived. Secondly, by LaSalles invariance principle, it is proved that the disease-free equilibrium is globally asymptotically stable when R 0 < 1 , and the disease dies out. By Routh-Hurwitz criterion theory, we also prove that the disease-free equilibrium is unstable and the unique endemic equilibrium is locally asymptotically stable when R 0 > 1 . Thirdly, by constructing a suitable Lyapunov function, we obtain that the unique endemic equilibrium is globally asymptotically stable and the disease persists at this endemic equilibrium if it initially exists when R 0 > 1 . Finally, some numerical simulations are presented to illustrate the analysis results.

Global dynamics of hepatitis C viral infection with logistic proliferation

2016 ◽  
Vol 09 (04) ◽  
pp. 1650056
Author(s):  
Sandip Banerjee ◽  
Ram Keval ◽  
Sunita Gakkhar
Keyword(s):  
Mathematical Model ◽  
Hepatitis C Virus ◽  
Stability Analysis ◽  
Hepatitis C ◽  
Viral Infection ◽  
Global Stability ◽  
Geometric Approach ◽  
Global Dynamics ◽  
Viral Dynamics ◽  
Global Stability Analysis

A modified mathematical model of hepatitis C viral dynamics has been presented in this paper, which is described by four coupled ordinary differential equations. The aim of this paper is to perform global stability analysis using geometric approach to stability, based on the higher-order generalization of Bendixson’s criterion. The result is also supported numerically. An important epidemiological issue of eradicating hepatitis C virus has been addressed through the global stability analysis.

scholarly journals Analysis of an HIV - HCV simultaneous infection model with time delay

2021 ◽  
pp. 1-11
Author(s):  
Adamu Shitu Hassan ◽  
Nafiu Hussaini
Keyword(s):  
Hepatitis C Virus ◽  
Hepatitis C ◽  
Time Delay ◽  
Numerical Simulations ◽  
Infection Model ◽  
Asymptotically Stable ◽  
Delay Model ◽  
Globally Asymptotically Stable ◽  
Simultaneous Infection ◽  
Disease Free

A novel mathematical delay model for simultaneous infection of HIV and hepatitis C virus is formulated and dynamically analyzed. Basic properties of the model are established and proved. Basic reproductive threshold is systematically calculated as the maximum of three subthreshold parameters. A disease free equilibrium is determined to be globally asymptotically stable for all values of the delay when the threshold is less than unity. However, when the threshold is greater than one, endemic equilibrium emerged which is shown to be locally asymptotically stable for any length of delay. Although the delay has no effect on stabilities of equilibria points, however, it is found to reduce the infectivity of the viruses as the length of the delay is increased. Epidemiological interpretations of the results and numerical simulations illustrating them are given.

scholarly journals Stability and Hopf Bifurcation for a Delayed SIR Epidemic Model with Logistic Growth

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Yakui Xue ◽  
Tiantian Li
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Threshold Value ◽  
Endemic Equilibrium ◽  
Logistic Growth ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Sir Epidemic Model ◽  
Globally Asymptotically Stable ◽  
Sir Epidemic

We study a delayed SIR epidemic model and get the threshold value which determines the global dynamics and outcome of the disease. First of all, for anyτ, we show that the disease-free equilibrium is globally asymptotically stable; whenR0<1, the disease will die out. Directly afterwards, we prove that the endemic equilibrium is locally asymptotically stable for anyτ=0; whenR0>1, the disease will persist. However, for anyτ≠0, the existence conditions for Hopf bifurcations at the endemic equilibrium are obtained. Besides, we compare the delayed SIR epidemic model with nonlinear incidence rate to the one with bilinear incidence rate. At last, numerical simulations are performed to illustrate and verify the conclusions.

Global Dynamics of a Holling-II Amensalism System with Nonlinear Growth Rate and Allee Effect on the First Species

2021 ◽  
Vol 31 (03) ◽  
pp. 2150050
Author(s):  
Demou Luo ◽  
Qiru Wang
Keyword(s):  
Growth Rate ◽  
Allee Effect ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Nonlinear Growth ◽  
Trivial Equilibrium ◽  
Existence And Stability ◽  
Stable Equilibria ◽  
Theoretical Results

Of concern is the global dynamics of a two-species Holling-II amensalism system with nonlinear growth rate. The existence and stability of trivial equilibrium, semi-trivial equilibria, interior equilibria and infinite singularity are studied. Under different parameters, there exist two stable equilibria which means that this model is not always globally asymptotically stable. Together with the existence of all possible equilibria and their stability, saddle connection and close orbits, we derive some conditions for transcritical bifurcation and saddle-node bifurcation. Furthermore, the global dynamics of the model is performed. Next, we incorporate Allee effect on the first species and offer a new analysis of equilibria and bifurcation discussion of the model. Finally, several numerical examples are performed to verify our theoretical results.

scholarly journals Building a mechanistic mathematical model of hepatitis C virus entry

2018 ◽  
Author(s):  
Mphatso Kalemera ◽  
Dilyana Mincheva ◽  
Joe Grove ◽  
Christopher J. R. Illingworth
Keyword(s):  
Mathematical Model ◽  
Hepatitis C Virus ◽  
Hepatitis C ◽  
Viral Entry ◽  
Productive Infection ◽  
Virus Particles ◽  
Quantitative Studies ◽  
Receptor Dynamics ◽  
Viral Lifecycle ◽  
The Impact

AbstractThe mechanism by which hepatitis C virus (HCV) gains entry into cells is a complex one, involving a broad range of host proteins. Entry is a critical phase of the viral lifecycle, and a potential target for therapeutic or vaccine-mediated intervention. However, the mechanics of HCV entry remain poorly understood. Here we describe a novel computational model of viral entry, encompassing the relationship between HCV and the key host receptors CD81 and SR-B1. We conduct experiments to thoroughly quantify the influence of an increase or decrease in receptor availability upon the extent of viral entry. We use these data to build and parameterise a mathematical model, which we then validate by further experiments. Our results are consistent with sequential HCV-receptor interactions, whereby initial interaction between the HCV E2 glycoprotein and SR-B1 facilitates the accumulation CD81 receptors, leading to viral entry. However, we also demonstrate that a small minority of virus can achieve entry in the absence of SR-B1. Our model estimates the impact of the different obstacles that viruses must surmount to achieve entry; among virus particles attaching to the cell surface, 20-35% accumulate sufficient CD81 receptors, of these 4-8% then complete the subsequent steps to achieve productive infection. Furthermore, we make estimates of receptor stoichiometry; between 3 and 6 CD81 receptors are likely to be required to achieve viral entry. Our model provides a tool to investigate the entry characteristics of HCV variants and outlines a framework for future quantitative studies of the multi-receptor dynamics of HCV entry.

scholarly journals Stability of an HIV/AIDS Treatment Model with Different Stages

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Hai-Feng Huo ◽  
Rui Chen
Keyword(s):  
Hiv Infection ◽  
Hiv Positive ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Treatment Model ◽  
Globally Asymptotically Stable ◽  
Asymptomatic Stage ◽  
Mathematical Analyses ◽  
Two Stages ◽  
Hiv Aids

An HIV/AIDS treatment model with different stages is proposed in this paper. The stage of the HIV infection is divided into two stages, that is, HIV-positive in the asymptomatic stage of HIV infection and HIV-positive individuals in the pre-AIDS stage. The fact that some individuals with HIV-positive individuals after the treatment can be transformed into the compartment of HIV-positive individuals in the asymptomatic stage of HIV infection, the compartment of HIV-positive individuals in the pre-AIDS stage, or the compartment of individuals with full-blown AIDS is also considered. Mathematical analyses establish the idea that the global dynamics of the HIV/AIDS model are determined by the basic reproduction numberR0. The disease-free equilibrium is globally asymptotically stable ifR0<1. The endemic equilibrium is globally asymptotically stable ifR0>1for a special case. Numerical simulations are also conducted to support the analytic results.

scholarly journals The genotype 3-specific hepatitis C virus core protein residue phenylalanine 164 increases steatosis in an in vitro cellular model

Gut ◽  
2007 ◽  
Vol 56 (9) ◽  
pp. 1302-1308 ◽  
Author(s):  
C Hourioux ◽  
R Patient ◽  
A Morin ◽  
E Blanchard ◽  
A Moreau ◽  
...  
Keyword(s):  
Hepatitis C Virus ◽  
Hepatitis C ◽  
Core Protein ◽  
Cellular Model ◽  
Genotype 3 ◽  
Virus Core

scholarly journals A MATHEMATICAL MODEL FOR EBOLA EPIDEMIC WITH SELF-PROTECTION MEASURES

2018 ◽  
Vol 26 (01) ◽  
pp. 107-131 ◽  
Author(s):  
T. BERGE ◽  
M. CHAPWANYA ◽  
J. M.-S. LUBUMA ◽  
Y. A. TEREFE
Keyword(s):  
Mathematical Model ◽  
Ebola Virus ◽  
Virus Disease ◽  
Mass Action ◽  
Transmission Dynamics ◽  
Asymptotically Stable ◽  
Protection Measures ◽  
Globally Asymptotically Stable ◽  
New Formulation ◽  
Self Protection

A mathematical model presented in Berge T, Lubuma JM-S, Moremedi GM, Morris N Shava RK, A simple mathematical model for Ebola in Africa, J Biol Dyn 11(1): 42–74 (2016) for the transmission dynamics of Ebola virus is extended to incorporate vaccination and change of behavior for self-protection of susceptible individuals. In the new setting, it is shown that the disease-free equilibrium is globally asymptotically stable when the basic reproduction number [Formula: see text] is less than or equal to unity and unstable when [Formula: see text]. In the latter case, the model system admits at least one endemic equilibrium point, which is locally asymptotically stable. Using the parameters relevant to the transmission dynamics of the Ebola virus disease, we give sensitivity analysis of the model. We show that the number of infectious individuals is much smaller than that obtained in the absence of any intervention. In the case of the mass action formulation with vaccination and education, we establish that the number of infectious individuals decreases as the intervention efforts increase. In the new formulation, apart from supporting the theory, numerical simulations of a nonstandard finite difference scheme that we have constructed suggests that the results on the decrease of the number of infectious individuals is valid.

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