Global Stability of a Delay Virus Dynamics Model with Mitotic Transmission and Cure Rate

Ávila-Vales, Eric; Canul-Pech, Abraham; García-Almeida, Gerardo E.; Pérez, Ángel

doi:10.1007/978-3-030-49896-2_4

Cited by 2 publications

(5 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We have needed another conditions to ensure the global stability for this equilibrium. Most of the results obtained in the present work generalize, in the same framework, those obtained by Eric Avila Vales et al in [1] in the sense that in [1] the proliferation rates of infected and uninfected hepatocytes are identical and the This work can be developed in many ways as follows:…”

Section: Discussionsupporting

confidence: 85%

“…In order to better understand the dynamics of HCV viral infection, this paper presents a mathematical study on the global dynamics of improved intra-host HCV models based on models in [2] and [1]. In this work we have established results about the local and global stability of equilibria known as infection free equilibrium and infection persist equilibrium.…”

Section: Discussionmentioning

confidence: 99%

“…The model (2.1) is a modification of model (2) studied in [2] and later in [1]. The features of the latter is as follows : H(t), I(t) and V (t) denote the concentration of uninfected hepatocytes (or target cells), infected hepatocytes and free virus, respectively.…”

Section: Model Constructionmentioning

confidence: 99%

“…Due to the severity of hepatitis C infection, it is necessary to develop the tools that help to understand this disease. It is for this reason that several mathematical models have been developed to better understand the dynamics of the hepatitis C virus within the liver itself [1,2,7,18,20,19,17]. Eric Avila Vales et al in [2] studied an intra-host delay model, which is a pioneer work which inspired the work in the present paper.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Global stability of a delay HCV dynamics model with cellular proliferation

Nangue

Tacteu

Guedlai³

2022

Math Appl Sci Eng

View full text Add to dashboard Cite

In this work, we propose and investigate a delay cell population model of hepatitis C virus (HCV) infection with cellular proliferation, absorption effect and a nonlinear incidence function. First of all, after having shown the existence of the local solutions of our model, we show the existence of the global solutions and positivity. Moreover, we determine the uninfected equilibrium point and the basic reproduction rate R0, which is a threshold number in mathematical epidemiology. After showing the existence and uniqueness of the infected equilibrium point, we proceed to the study of the local and global stability of this equilibrium. We show that if R0 < 1, the uninfected equilibrium point is globally asymptotically stable, which means that the disease will disappear and if R0 > 1, we have a unique infected equilibrium that is globally asymptotically stable under some conditions. Finally, we perform some numerical simulations to illustrate the obtained theoretical results.

show abstract

Section: Discussionsupporting

confidence: 85%

Section: Discussionmentioning

confidence: 99%

Section: Model Constructionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Global stability of a delay HCV dynamics model with cellular proliferation

Nangue

Tacteu

Guedlai³

2022

Math Appl Sci Eng

View full text Add to dashboard Cite

show abstract

“…The mathematical modeling in a patient allows a better understanding of the transmission of diseases and thus improves the strategies for their eradication. On the basis of the virus infection models proposed in [ 1 – 3 , 6 , 9 – 13 , 17 – 22 , 24 – 35 , 35 – 37 ], several mathematical models were examined and that are valuable for obtaining comprehensive knowledge about virus dynamics, for example models in the form of Ordinary Differential Equations (ODEs) [ 19 – 21 , 34 , 37 ], Delayed Differential Equations (DDE) [ 1 , 22 ], Partial Differential Equations (PDE) [ 4 , 29 , 32 , 35 ] and Fractional Differential Equations (FODE) [ 2 , 3 , 17 , 25 ].…”

Section: Introductionmentioning

confidence: 99%

A class of diffusive delayed viral infection models with general incidence function and cellular proliferation

Nangue

Fokam

2022

Arab. J. Math.

View full text Add to dashboard Cite

We propose and analyze a new class of three dimensional space models that describes infectious diseases caused by viruses such as hepatitis B virus (HBV) and hepatitis C virus (HCV). This work constructs a Reaction–Diffusion-Ordinary Differential Equation model of virus dynamics, including absorption effect, cell proliferation, time delay, and a generalized incidence rate function. By constructing suitable Lyapunov functionals, we show that the model has threshold dynamics: if the basic reproduction number $$\mathcal {R}_{0}(\tau ) \le 1 $$ R 0 ( τ ) ≤ 1 , then the uninfected equilibrium is globally asymptotically stable, whereas if $$\mathcal {R}_{0}(\tau ) > 1$$ R 0 ( τ ) > 1 , and under certain conditions, the infected equilibrium is globally asymptotically stable. This precedes a careful study of local asymptotic stability. We pay particular attention to prove boundedness, positivity, existence and uniqueness of the solution to the obtained initial and boundary value problem. Finally, we perform some numerical simulations to illustrate the theoretical results obtained in one-dimensional space. Our results improve and generalize some known results in the framework of virus dynamics.

show abstract

Global Stability of a Delay Virus Dynamics Model with Mitotic Transmission and Cure Rate

Cited by 2 publications

References 29 publications

Global stability of a delay HCV dynamics model with cellular proliferation

Global stability of a delay HCV dynamics model with cellular proliferation

A class of diffusive delayed viral infection models with general incidence function and cellular proliferation

Contact Info

Product

Resources

About