scholarly journals Stability Analysis for a Fractional HIV Infection Model with Nonlinear Incidence

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Linli Zhang ◽  
Gang Huang ◽  
Anping Liu ◽  
Ruili Fan
Keyword(s):  
Population Dynamics ◽  
Stability Analysis ◽  
Hiv Infection ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Nonnegative Solution ◽  
Infection Model ◽  
Nonlinear Incidence ◽  
Hiv Infection Model ◽  
The Stability

We introduce the fractional-order derivatives into an HIV infection model with nonlinear incidence and show that the established model in this paper possesses nonnegative solution, as desired in any population dynamics. We also deal with the stability of the infection-free equilibrium, the immune-absence equilibrium, and the immune-presence equilibrium. Numerical simulations are carried out to illustrate the results.

scholarly journals Global Exponential Stability of a Delayed HIV Infection Model with a Nonlinear Incidence Rate

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Zhiwen Long
Keyword(s):  
Stability Analysis ◽  
Hiv Infection ◽  
Exponential Stability ◽  
Incidence Rate ◽  
Infection Model ◽  
Target Cells ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Virus Particles ◽  
Hiv Infection Model

Under the assumption that there is a time delay between the time target cells are contacted by the virus particles and the time the contacted cells become actively infected, we investigate the exponential stability of the noninfected equilibrium for a delayed HIV infection model with a nonlinear incidence rate. Compared with the global asymptotic stability analysis based on basic reproduction number, exponential stability analysis reveals the change range of various cells in different time periods.

Stability and Hopf Bifurcation for a HIV Infection Model with Delayed Immune Response

2013 ◽  
Vol 641-642 ◽  
pp. 808-811
Author(s):  
Xiao Zhang ◽  
Dong Wei Huang ◽  
Yong Feng Guo
Keyword(s):  
Immune Response ◽  
Hopf Bifurcation ◽  
Asymptotic Stability ◽  
Hiv Infection ◽  
Numerical Simulations ◽  
Global Asymptotic Stability ◽  
Infection Model ◽  
Immune State ◽  
Hiv Infection Model ◽  
The Stability

In this paper, a class of HIV infection model with delayed immune response has been studied. We analyze the global asymptotic stability of the viral free equilibrium, and the stability and Hopf bifurcation of the infected equilibrium have been studied. Numerical simulations are carried out to explain the results of the analysis, and the change of the immune response of CTLs infects stability of system. These results can explain the complexity of the immune state of AIDs.

scholarly journals Dynamics of a Fractional Order HIV Infection Model with Specific Functional Response and Cure Rate

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Adnane Boukhouima ◽  
Khalid Hattaf ◽  
Noura Yousfi
Keyword(s):  
Hiv Infection ◽  
Functional Response ◽  
Fractional Order ◽  
Infection Model ◽  
Cure Rate ◽  
Order Model ◽  
Immunodeficiency Virus ◽  
Hiv Infection Model ◽  
Well Posed ◽  
Theoretical Results

We propose a fractional order model in this paper to describe the dynamics of human immunodeficiency virus (HIV) infection. In the model, the infection transmission process is modeled by a specific functional response. First, we show that the model is mathematically and biologically well posed. Second, the local and global stabilities of the equilibria are investigated. Finally, some numerical simulations are presented in order to illustrate our theoretical results.

scholarly journals Analisis Dinamik Model Transmisi COVID-19 dengan Melibatkan Intervensi Karantina

2021 ◽  
Author(s):  
Resmawan Resmawan ◽  
Agusyarif Rezka Nuha ◽  
Lailany Yahya
Keyword(s):  
Population Dynamics ◽  
Stability Analysis ◽  
Numerical Simulations ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Asymptotically Stable ◽  
Human Class ◽  
Existence Of Equilibrium ◽  
The Stability ◽  
Disease Free

This paper discusses the dynamics of COVID-19 transmission by involving quarantine interventions. The model was constructed by involving three classes of infectious causes, namely the exposed human class, asymptotically infected human class, and symptomatic infected human class. Variables were representing quarantine interventions to suppress infection growth were also considered in the model. Furthermore, model analysis is focused on the existence of equilibrium points and numerical simulations to visually showed population dynamics. The constructed model forms the SEAQIR model which has two equilibrium points, namely a disease-free equilibrium point and an endemic equilibrium point. The stability analysis showed that the disease-free equilibrium point was locally asymptotically stable at R0<1 and unstable at R0>1. Numerical simulations showed that increasing interventions in the form of quarantine could contribute to slowing the transmission of COVID-19 so that it is hoped that it can prevent outbreaks in the population.

A delayed HIV infection model with specific nonlinear incidence rate and cure of infected cells in eclipse stage

2016 ◽  
Vol 10 ◽  
pp. 2121-2130
Author(s):  
Mehdi Maziane ◽  
El Mehdi Lotfi ◽  
Marouane Mahrouf ◽  
Khalid Hattaf ◽  
Noura Yousfi
Keyword(s):  
Hiv Infection ◽  
Incidence Rate ◽  
Infection Model ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Infected Cells ◽  
Hiv Infection Model

scholarly journals Stability Analysis of Mathematical Model on HIV Infection with the Effects of Antiretroviral therapy

2020 ◽  
Vol 17 (1) ◽  
pp. 109-116
Author(s):  
Lilis Dwi Sapta Aprilyani ◽  
Kasbawati Kasbawati ◽  
Syamsuddin Toaha
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Antiretroviral Therapy ◽  
Hiv Infection ◽  
Protease Inhibitor ◽  
Equilibrium Points ◽  
Genetic Material ◽  
Infection Model ◽  
Antiretroviral Therapies ◽  
Hiv Infection Model

HIV is a retrovirus, a virus which has enzymes and can convert genetic material from RNA to DNA. Antiretroviral therapies are the treatment to make the activity of the virus slow. The purpose of this article is to develop a mathematical model of HIV infection by reviewing antiretroviral therapy, analyze the equilibrium point, and determine the effectiveness of antiretroviral therapy. There are two equilibrium points in this HIV infection model, namely infection-free equilibrium and infected equilibrium. Numerical simulations are carried out based on selected parameters showed that infection free equilibrium is reached when the effectiveness of antiretroviral therapy is 0,4 for RT inhibitor and 0,3 for Protease Inhibitor. This means that antiretroviral therapy may change infected conditions to infection free conditions.

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