Global Properties of Viral Infection Model with General Incidence Rate Function and Two Distributed Delays

2015 ◽  
Vol 12 (10) ◽  
pp. 3566-3571
Author(s):  
N. H. AlShamrani ◽  
A. M. Elaiw ◽  
M. A. Alghamdi
Keyword(s):  
Viral Infection ◽  
Incidence Rate ◽  
Rate Function ◽  
Distributed Delays ◽  
Infection Model ◽  
Global Properties ◽  
General Incidence Rate ◽  
Viral Infection Model

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 Global stability of a distributed delayed viral model with general incidence rate

2018 ◽  
Vol 16 (1) ◽  
pp. 1374-1389
Author(s):  
Eric Ávila-Vales ◽  
Abraham Canul-Pech ◽  
Erika Rivero-Esquivel
Keyword(s):  
Immune Response ◽  
Viral Infection ◽  
Global Stability ◽  
Numerical Simulations ◽  
Incidence Rate ◽  
Existence And Uniqueness ◽  
Lyapunov Functional ◽  
Infection Model ◽  
General Incidence Rate ◽  
Viral Infection Model

AbstractIn this paper, we discussed a infinitely distributed delayed viral infection model with nonlinear immune response and general incidence rate. We proved the existence and uniqueness of the equilibria. By using the Lyapunov functional and LaSalle invariance principle, we obtained the conditions of global stabilities of the infection-free equilibrium, the immune-exhausted equilibrium and the endemic equilibrium. Numerical simulations are given to verify the analytical results.

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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