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 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.

Bio-inspired computational heuristics to study models of HIV infection of CD4+ T-cell

2018 ◽  
Vol 11 (02) ◽  
pp. 1850019 ◽  
Author(s):  
Muhammad Asif Zahoor Raja ◽  
Kiran Asma ◽  
Muhammad Saeed Aslam
Keyword(s):  
T Cell ◽  
Hiv Infection ◽  
Cell Model ◽  
Hybrid Approach ◽  
Approximate Solutions ◽  
Infection Model ◽  
Ann Model ◽  
Infected Cells ◽  
Hiv Infection Model ◽  
Numerical Solver

In this work, biologically-inspired computing framework is developed for HIV infection of CD4[Formula: see text] T-cell model using feed-forward artificial neural networks (ANNs), genetic algorithms (GAs), sequential quadratic programming (SQP) and hybrid approach based on GA-SQP. The mathematical model for HIV infection of CD4[Formula: see text] T-cells is represented with the help of initial value problems (IVPs) based on the system of ordinary differential equations (ODEs). The ANN model for the system is constructed by exploiting its strength of universal approximation. An objective function is developed for the system through unsupervised error using ANNs in the mean square sense. Training with weights of ANNs is carried out with GAs for effective global search supported with SQP for efficient local search. The proposed scheme is evaluated on a number of scenarios for the HIV infection model by taking the different levels for infected cells, natural substitution rates of uninfected cells, and virus particles. Comparisons of the approximate solutions are made with results of Adams numerical solver to establish the correctness of the proposed scheme. Accuracy and convergence of the approach are validated through the results of statistical analysis based on the sufficient large number of independent runs.

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.

Stability analysis for delayed viral infection model with multitarget cells and general incidence rate

2015 ◽  
Vol 09 (01) ◽  
pp. 1650007 ◽  
Author(s):  
Jinliang Wang ◽  
Xinxin Tian ◽  
Xia Wang
Keyword(s):  
Viral Infection ◽  
Incidence Rate ◽  
Time Delays ◽  
Infection Model ◽  
Target Cells ◽  
Uniform Persistence ◽  
Nonlinear Incidence Rate ◽  
General Incidence Rate ◽  
Infected Cells ◽  
Viral Infection Model

In this paper, the sharp threshold properties of a (2n + 1)-dimensional delayed viral infection model are investigated. This model combines with n classes of uninfected target cells, n classes of infected cells and nonlinear incidence rate h(x, v). Two kinds of distributed time delays are incorporated into the model to describe the time needed for infection of uninfected target cells and virus replication. Under certain conditions, it is shown that the basic reproduction number is a threshold parameter for the existence of the equilibria, uniform persistence, as well as for global stability of the equilibria of the model.

scholarly journals Stability and Hopf Bifurcation in a Delayed HIV Infection Model with General Incidence Rate and Immune Impairment

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Fuxiang Li ◽  
Wanbiao Ma ◽  
Zhichao Jiang ◽  
Dan Li
Keyword(s):  
Hiv Infection ◽  
Incidence Rate ◽  
Reproduction Number ◽  
Dynamical Behavior ◽  
Infection Model ◽  
Ctl Response ◽  
General Incidence Rate ◽  
Immune Impairment ◽  
Hiv Infection Model ◽  
The Stability

We investigate the dynamical behavior of a delayed HIV infection model with general incidence rate and immune impairment. We derive two threshold parameters, the basic reproduction numberR0and the immune response reproduction numberR1. By using Lyapunov functional and LaSalle invariance principle, we prove the global stability of the infection-free equilibrium and the infected equilibrium without immunity. Furthermore, the existence of Hopf bifurcations at the infected equilibrium with CTL response is also studied. By theoretical analysis and numerical simulations, the effect of the immune impairment rate on the stability of the infected equilibrium with CTL response has been studied.

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