scholarly journals Mathematical Analysis of HIV Models with Switching Nonlinear Incidence Functions and Pulse Control

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Xiying Wang ◽  
Wei Xu ◽  
Yujun Cui ◽  
Xiaomei Wang
Keyword(s):  
Sufficient Conditions ◽  
The Novel ◽  
Pulse Control ◽  
Future Directions ◽  
Nonlinear Incidence ◽  
Pulse Vaccination ◽  
Immunodeficiency Virus ◽  
Functional Forms ◽  
Incidence Functions ◽  
Realistic Significance

This paper aims to study the dynamics of new HIV (the human immunodeficiency virus) models with switching nonlinear incidence functions and pulse control. Nonlinear incidence functions are first assumed to be time-varying functions and switching functional forms in time, which have more realistic significance to model infectious disease models. New threshold conditions with the periodic switching term are obtained to guarantee eradication of the disease, by using the novel type of common Lyapunov function. Furthermore, pulse vaccination is applied to the above model, and new sufficient conditions for the eradication of the disease are presented in terms of the pulse effect and the switching effect. Finally, several numerical examples are given to show the effectiveness of the proposed results, and future directions are put forward.

THE DYNAMICS OF HIV MODELS WITH SWITCHING PARAMETERS AND PULSE CONTROL

2016 ◽  
Vol 24 (04) ◽  
pp. 385-407
Author(s):  
XIYING WANG ◽  
XINZHI LIU ◽  
WEI XU ◽  
WEI-CHAU XIE ◽  
WANPING LIU
Keyword(s):  
Viral Suppression ◽  
Control Strategies ◽  
Vaccination Strategy ◽  
Pulse Control ◽  
Dynamics Model ◽  
Virus Elimination ◽  
Future Directions ◽  
Immunodeficiency Virus ◽  
Threshold Conditions ◽  
Infected Cells

This paper studies some human immunodeficiency virus (HIV) models with switching parameters and pulse control. The classical virus dynamics model is first modified by incorporating switching parameters which are assumed to be time-varying. Some threshold conditions are derived to guarantee the virus elimination by utilizing a Razumikhin-type approach. The results show that the proper switching conditions chosen can increase the counts of CD4+T-cells while reducing viral load. Pulse control strategies are then applied to the above model. More precisely, the treatment strategy and the vaccination strategy are applied to infected cells and uninfected cells, respectively. Each control strategy is analyzed to gauge its success in achieving viral suppression. Numerical simulations are performed to complement the analytical results and motivate future directions.

scholarly journals Threshold Dynamics of the Switched Multicity Epidemic Models with Pulse Control

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Xiying Wang ◽  
Wei Xu ◽  
Wenfeng Wang
Keyword(s):  
Control Strategies ◽  
Immune Deficiency Syndrome ◽  
Deficiency Syndrome ◽  
Epidemic Models ◽  
Threshold Dynamics ◽  
Pulse Control ◽  
Susceptible Population ◽  
Immunodeficiency Virus ◽  
Sexual Contacts ◽  
Functional Forms

This paper mainly studies the threshold dynamics of new multicity HIV (Human Immunodeficiency Virus) epidemic models with switching parameters and pulse control. The model’s parameters are assumed to be time-varying functions and switching functional forms in time due to seasonal changes. And the susceptible population is assumed to become infected via shared injections or sexual contacts with infected individuals and pre-AIDS patients (following infection with HIV but before the full development of acquired immune deficiency syndrome). New threshold conditions are established to ensure the extinction of the disease by using Razumikhin-type approach. Pulse control strategies are then applied to the multicity epidemic model and analyzed to guarantee their success in eradicating the disease. Numerical examples are performed to support the analytical results.

Data-driven tracking consensus for a class of unknown nonlinear multi-agent systems

2021 ◽  
pp. 107754632110340
Author(s):  
Jia Wu ◽  
Ning Liu ◽  
Wenyan Tang
Keyword(s):  
Control Method ◽  
Sufficient Conditions ◽  
Data Driven ◽  
The Novel ◽  
Multi Agent Systems ◽  
Tracking Errors ◽  
Agent Systems ◽  
Model Free ◽  
Strongly Connected ◽  
Multi Agent

This study investigates the tracking consensus problem for a class of unknown nonlinear multi-agent systems A novel data-driven protocol for this problem is proposed by using the model-free adaptive control method To obtain faster convergence speed, one-step-ahead desired signal is introduced to construct the novel protocol Here, switching communication topology is considered, which is not required to be strongly connected all the time Through rigorous analysis, sufficient conditions are given to guarantee that the tracking errors of all agents are convergent under the novel protocol Examples are given to validate the effectiveness of results derived in this article

scholarly journals Finite-time stability of $ q $-fractional damped difference systems with time delay

2021 ◽  
Vol 6 (11) ◽  
pp. 12011-12027
Author(s):  
Jingfeng Wang ◽  
◽  
Chuanzhi Bai
Keyword(s):  
Time Delay ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Gronwall Inequality ◽  
The Novel ◽  
Delayed Systems ◽  
Finite Time Stability ◽  
Difference Systems ◽  
Grönwall Inequality ◽  
Uniqueness Of The Solution

<abstract><p>In this paper, we investigate and obtain a new discrete $ q $-fractional version of the Gronwall inequality. As applications, we consider the existence and uniqueness of the solution of $ q $-fractional damped difference systems with time delay. Moreover, we formulate the novel sufficient conditions such that the $ q $-fractional damped difference delayed systems is finite time stable. Our result extend the main results of the paper by Abdeljawad et al. [A generalized $ q $-fractional Gronwall inequality and its applications to nonlinear delay $ q $-fractional difference systems, J.Inequal. Appl. 2016,240].</p></abstract>

scholarly journals Can common coronavirus compete with novel coronavirus？

2020 ◽  
Author(s):  
ZHONGNENG XU
Keyword(s):  
Resource Competition ◽  
Respiratory Infections ◽  
Medical Application ◽  
Theoretical Implication ◽  
Research Area ◽  
The Novel ◽  
Immunodeficiency Virus ◽  
The Common ◽  
Novel Coronavirus ◽  
Virus Interactions

The novel coronavirus, SARS-CoV-2, caused lethal human respiratory infections, and there is a big problem to control the disease. The application of other viruses to compete with the novel coronavirus was proposed in this paper. On the viewpoint of receptor competition, resource competition, and cross immunity, an attempt should be made to select a natural virus, such as the common coronavirus causing the common cold in human, or transform a virus with biotechnology in order to resist the novel coronavirus. Similar scenarios were suggested to deal with other viruses like human immunodeficiency virus. Microecological communities of viruses could form an independent research area to dig the deeper biological and medical significance. The present study provided the information to further the theoretical implication and medical application of the study of virus interactions.

scholarly journals Stability Analysis for Discrete-Time Stochastic Fuzzy Neural Networks with Mixed Delays

2019 ◽  
Vol 2019 ◽  
pp. 1-13
Author(s):  
YaJun Li ◽  
Quanxin Zhu
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Fuzzy Neural Networks ◽  
Linear Matrix ◽  
Mixed Delays ◽  
The Novel ◽  
Free Weight ◽  
Fuzzy Neural ◽  
The Stability

This paper is concerned with the stability problem of a class of discrete-time stochastic fuzzy neural networks with mixed delays. New Lyapunov-Krasovskii functions are proposed and free weight matrices are introduced. The novel sufficient conditions for the stability of discrete-time stochastic fuzzy neural networks with mixed delays are established in terms of linear matrix inequalities (LMIs). Finally, numerical examples are given to illustrate the effectiveness and benefits of the proposed method.

scholarly journals Constructing chaotic transformations with closed functional forms

2006 ◽  
Vol 2006 ◽  
pp. 1-16 ◽  
Author(s):  
Weihong Huang
Keyword(s):  
Computer Simulations ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Functional Forms ◽  
Necessary And Sufficient

The properties of complete chaotic unimodal transformations with closed functional forms are examined and the necessary and sufficient conditions are provided to construct such transformations. Theoretical findings are verified with computer simulations.

scholarly journals Meningeal Lymphatics: A Review and Future Directions From a Clinical Perspective

2019 ◽  
Vol 14 ◽  
pp. 117906951988902 ◽  
Author(s):  
Korri S Hershenhouse ◽  
Orr Shauly ◽  
Daniel J Gould ◽  
Ketan M Patel
Keyword(s):  
Potential Role ◽  
Immune Surveillance ◽  
Lymphatic Vessels ◽  
Anatomical Structure ◽  
The Novel ◽  
Clinical Perspective ◽  
Future Directions ◽  
Drainage Patterns ◽  
Current State ◽  
The Central Nervous System

The recent discovery of lymphatic vessels in the meningeal layers calls into question the known mechanisms of fluid and macromolecule homeostasis and immunoregulation within the central nervous system. These meningeal lymphatic vessels and their potential role in the pathophysiology of neurological disease have become a rapidly expanding area of research, with the hopes that they may provide a novel therapeutic target in the treatment of many devastating conditions. This article reviews the current state of knowledge surrounding the anatomical structure of the vessels, their functions in fluid and solute transport and immune surveillance, as well as their studied developmental biology, relationship with the novel hypothesized “glymphatic” system, and implications in neurodegenerative disease in animal models. Furthermore, this review summarizes findings from the human studies conducted thus far regarding the presence, anatomy, and drainage patterns of meningeal lymphatic vessels and discusses, from a clinical perspective, advancements in both imaging technologies and interventional methodologies used to access ultrafine peripheral lymphatic vessels.

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