Global analysis of a humoral and cellular immunity virus dynamics model with the Beddington-DeAngelis incidence rate

2014 ◽  
Vol 38 (14) ◽  
pp. 2984-2993 ◽  
Author(s):  
Yongmei Su ◽  
Deshun Sun ◽  
Lei Zhao
Keyword(s):  
Incidence Rate ◽  
Cellular Immunity ◽  
Global Analysis ◽  
Virus Dynamics ◽  
Dynamics Model ◽  
Humoral And Cellular Immunity

A Delay Virus Dynamics Model with General Incidence Rate

2013 ◽  
Vol 22 (2) ◽  
pp. 181-190 ◽  
Author(s):  
Khalid Hattaf ◽  
Noura Yousfi ◽  
Abdessamad Tridane
Keyword(s):  
Incidence Rate ◽  
Virus Dynamics ◽  
Dynamics Model ◽  
General Incidence Rate

scholarly journals Global Analysis of a Virus Dynamics Model with General Incidence Function and Cure Rate

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Yu Yang
Keyword(s):  
Reproduction Number ◽  
Global Analysis ◽  
Logistic Function ◽  
Virus Dynamics ◽  
Asymptotically Stable ◽  
Cure Rate ◽  
Dynamics Model ◽  
Globally Asymptotically Stable ◽  
Incidence Function ◽  
Stable Periodic

A virus dynamics model with logistic function, general incidence function, and cure rate is considered. By carrying out mathematical analysis, we show that the infection-free equilibrium is globally asymptotically stable if the basic reproduction numberℛ0≤1. Ifℛ0>1, then the infection equilibrium is globally asymptotically stable under some assumptions. Furthermore, we also obtain the conditions for which the model exists an orbitally asymptotically stable periodic solution. Examples are provided to support our analytical conclusions.

GLOBAL ANALYSIS OF AN EXTENDED HIV DYNAMICS MODEL WITH GENERAL INCIDENCE RATE

2015 ◽  
Vol 23 (03) ◽  
pp. 401-421
Author(s):  
AHMED ELAIW ◽  
NADA. ALMUALLEM ◽  
XIA WANG
Keyword(s):  
Global Stability ◽  
Incidence Rate ◽  
Global Analysis ◽  
Drug Efficacy ◽  
Target Cells ◽  
Qualitative Behavior ◽  
Global Dynamics ◽  
Dynamics Model ◽  
Hiv Dynamics ◽  
Infected Cells

The objective of this work is to investigate the qualitative behavior of an Human Immunodeficiency Virus (HIV) dynamics model with two types of cocirculating target cells and under the effect of anti-viral drug therapy. The model takes into account both short-lived infected cells and long-lived chronically infected cells. In the two types of target cells, the drug efficacy is assumed to be different. The incidence rate of virus infection is given by general functional response. We have derived the basic reproduction number which determines the global dynamics of the model. We have established a set of conditions which are sufficient to investigate the global stability of the equilibria of the model. The global stability analysis of the model has been established using the Lyapunov method. Numerical simulations have been performed for the model with a specific form of the incidence rate function. We have shown that the numerical and theoretical results are consistent.

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