scholarly journals Global stability of an adaptive immunity HIV dynamics model with silent and active cell-to-cell transmissions

AIP Advances ◽  
2020 ◽  
Vol 10 (8) ◽  
pp. 085216
Author(s):  
A. M. Elaiw ◽  
N. H. AlShamrani ◽  
A. D. Hobiny ◽  
I. A. Abbas
Keyword(s):  
Global Stability ◽  
Adaptive Immunity ◽  
Active Cell ◽  
Dynamics Model ◽  
Hiv Dynamics

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.

scholarly journals Global Stability of Malaria Transmission Dynamics Model with Logistic Growth

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Abadi Abay Gebremeskel
Keyword(s):  
Sensitivity Analysis ◽  
Global Stability ◽  
Malaria Transmission ◽  
Equilibrium Points ◽  
Transmission Dynamics ◽  
Logistic Growth ◽  
Asymptotically Stable ◽  
Dynamics Model ◽  
Globally Asymptotically Stable ◽  
The Impact

Mathematical models become an important and popular tools to understand the dynamics of the disease and give an insight to reduce the impact of malaria burden within the community. Thus, this paper aims to apply a mathematical model to study global stability of malaria transmission dynamics model with logistic growth. Analysis of the model applies scaling and sensitivity analysis and sensitivity analysis of the model applied to understand the important parameters in transmission and prevalence of malaria disease. We derive the equilibrium points of the model and investigated their stabilities. The results of our analysis have shown that if R0≤1, then the disease-free equilibrium is globally asymptotically stable, and the disease dies out; if R0>1, then the unique endemic equilibrium point is globally asymptotically stable and the disease persists within the population. Furthermore, numerical simulations in the application of the model showed the abrupt and periodic variations.

scholarly journals Global Properties of a General Latent Pathogen Dynamics Model with Delayed Pathogenic and Cellular Infections

2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
A. M. Elaiw ◽  
A. A. Almatrafi ◽  
A. D. Hobiny ◽  
K. Hattaf
Keyword(s):  
Global Stability ◽  
Infection Model ◽  
Global Dynamics ◽  
Dynamics Model ◽  
Pathogen Dynamics ◽  
Global Properties ◽  
Latently Infected ◽  
Infected Cells ◽  
Theoretical Results ◽  
Pathogenic Infection

This paper studies the global dynamics of a general pathogenic infection model with two ways of infections. The effect of antibody immune response is analyzed. We incorporate three discrete time delays and both latently infected cells and actively infected cells. The infection rate and production and clearance/death rates of the cells and pathogens are given by general functions. We determine two threshold parameters to investigate the global stability of three equilibria. We use Lyapunov method to establish the global stability. We support our theoretical results by numerical simulations.

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