The threshold for a stochastic HIV-1 infection model with Beddington-DeAngelis incidence rate

2018 ◽  
Vol 64 ◽  
pp. 168-184 ◽  
Author(s):  
Chunyan Ji
Keyword(s):  
Incidence Rate ◽  
Infection Model ◽  
Hiv 1

scholarly journals Global Stability of an HIV-1 Infection Model with General Incidence Rate and Distributed Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Abdoul Samba Ndongo ◽  
Hamad Talibi Alaoui
Keyword(s):  
Incidence Rate ◽  
Viral Entry ◽  
Disease Transmission ◽  
Transmission Function ◽  
Infection Model ◽  
Global Dynamics ◽  
General Incidence Rate ◽  
Delay Differential ◽  
Hiv 1 ◽  
Intracellular Delays

In this work an HIV-1 infection model with nonlinear incidence rate and distributed intracellular delays and with humoral immunity is investigated. The disease transmission function is assumed to be governed by general incidence rate f(T,V)V. The intracellular delays describe the time between viral entry into a target cell and the production of new virus particles and the time between infection of a cell and the emission of viral particle. Lyapunov functionals are constructed and LaSalle invariant principle for delay differential equation is used to establish the global asymptotic stability of the infection-free equilibrium, infected equilibrium without B cells response, and infected equilibrium with B cells response. The results obtained show that the global dynamics of the system depend on both the properties of the general incidence function and the value of certain threshold parameters R0 and R1 which depends on the delays.

A delayed HIV-1 infection model with Beddington–DeAngelis functional response

2010 ◽  
Vol 62 (1-2) ◽  
pp. 67-72 ◽  
Author(s):  
Xia Wang ◽  
Youde Tao ◽  
Xinyu Song
Keyword(s):  
Functional Response ◽  
Infection Model ◽  
Hiv 1

scholarly journals Determination of Number of Infected Cells and Concentration of Viral Particles in Plasma during HIV-1 Infections Using Shehu Transformation

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
M. Higazy ◽  
Sudhanshu Aggarwal ◽  
Y. S. Hamed
Keyword(s):  
Initial Conditions ◽  
Integral Transformation ◽  
Mathematical Representation ◽  
Infection Model ◽  
Viral Particles ◽  
Infected Cells ◽  
Linear Differential ◽  
The Mathematical Model ◽  
Ordinary Linear Differential Equations ◽  
Hiv 1

In this paper, the authors determine the number of infected cells and concentration of infected (viral) particles in plasma during HIV-1 (human immunodeficiency virus type one) infections using Shehu transformation. For this, the authors first defined some useful properties of Shehu transformation with proof and then applied Shehu transformation on the mathematical representation of the HIV-1 infection model. The mathematical model of HIV-1 infections contains a system of two simultaneous ordinary linear differential equations with initial conditions. Results depict that Shehu transformation is very effective integral transformation for determining the number of infected cells and concentration of viral particles in plasma during HIV-1 infections.

scholarly journals Analysis and computation of multi-pathways and multi-delays HIV-1 infection model

2018 ◽  
Vol 54 ◽  
pp. 517-536 ◽  
Author(s):  
Debadatta Adak ◽  
Nandadulal Bairagi
Keyword(s):  
Infection Model ◽  
Hiv 1

scholarly journals Spatial and Temporal Dynamics of a Viral Infection Model with Two Nonlocal Effects

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-20 ◽  
Author(s):  
Xiaoyan Wang ◽  
Yuming Chen ◽  
Junyuan Yang
Keyword(s):  
Steady State ◽  
Viral Infection ◽  
Incidence Rate ◽  
Temporal Dynamics ◽  
Principal Eigenvalue ◽  
Semigroup Theory ◽  
Infection Model ◽  
Nonlocal Effects ◽  
Backward Euler ◽  
Viral Infection Model

We propose and study a viral infection model with two nonlocal effects and a general incidence rate. First, the semigroup theory and the classical renewal process are adopted to compute the basic reproduction number R0 as the spectral radius of the next-generation operator. It is shown that R0 equals the principal eigenvalue of a linear operator associated with a positive eigenfunction. Then we obtain the existence of endemic steady states by Shauder fixed point theorem. A threshold dynamics is established by the approach of Lyapunov functionals. Roughly speaking, if R0<1, then the virus-free steady state is globally asymptotically stable; if R0>1, then the endemic steady state is globally attractive under some additional conditions on the incidence rate. Finally, the theoretical results are illustrated by numerical simulations based on a backward Euler method.

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