scholarly journals The impact of nonlinear perturbation to the dynamics of HIV model

2021 ◽  
Author(s):  
Zhenfeng Shi ◽  
Daqing Jiang ◽  
Ningzhong Shi ◽  
Tasawar Hayat ◽  
Ahmed Alsaedi
Keyword(s):  
Hiv Infection ◽  
Stochastic Model ◽  
Numerical Simulations ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Nonlinear Perturbation ◽  
Rigorous Analysis ◽  
Hiv Model ◽  
The Impact ◽  
Theoretical Results

In this paper, we developed and studied a stochastic HIV model with nonlinear perturbation. Through a rigorous analysis, we firstly showed that the solution of the stochastic model is positive and global. Then, by employing suitable stochastic Lyapunov functions, we prove that the stochastic model admit a unique ergodic stationary distribution. In addition, sufficient conditions for the extinction of HIV infection are derived. Finally, numerical simulations are employed to confirm our theoretical results.

scholarly journals Asymptotic Behavior Analysis for a Three-Species Food Chain Stochastic Model with Regime Switching

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Junmei Liu ◽  
Yonggang Ma
Keyword(s):  
Asymptotic Behavior ◽  
Lyapunov Function ◽  
Stochastic Model ◽  
Numerical Simulations ◽  
Behavior Analysis ◽  
Food Chain ◽  
Regime Switching ◽  
Sufficient Conditions ◽  
Stationary Distributions ◽  
Theoretical Results

This paper discusses the asymptotic behavior of a class of three-species stochastic model with regime switching. Using the Lyapunov function, we first obtain sufficient conditions for extinction and average time persistence. Then, we prove sufficient conditions for the existence of stationary distributions of populations, and they are ergodic. Numerical simulations are carried out to support our theoretical results.

scholarly journals An LMI Approach to Stability for Linear Time-Varying System with Nonlinear Perturbation on Time Scales

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Kanit Mukdasai ◽  
Piyapong Niamsup
Keyword(s):  
Time Scales ◽  
Lyapunov Functions ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Nonlinear Perturbation ◽  
Uniform Stability ◽  
Time Varying ◽  
Lmi Approach ◽  
Theoretical Results

We consider Lyapunov stability theory of linear time-varying system and derive sufficient conditions for uniform stability, uniform exponential stability, -uniform stability, andh-stability for linear time-varying system with nonlinear perturbation on time scales. We construct appropriate Lyapunov functions and derive several stability conditions. Numerical examples are presented to illustrate the effectiveness of the theoretical results.

scholarly journals Detectable sensation of a stochastic smoking model

2020 ◽  
Vol 18 (1) ◽  
pp. 1045-1055
Author(s):  
Abdullah Alzahrani ◽  
Anwar Zeb
Keyword(s):  
Stochastic Model ◽  
Numerical Simulations ◽  
Sufficient Conditions

Abstract This paper is related to the stochastic smoking model for the purpose of creating the effects of smoking that are not observed in deterministic form. First, formulation of the stochastic model is presented. Then the sufficient conditions for extinction and persistence are determined. Furthermore, the threshold of the proposed stochastic model is discussed, when noises are small or large. Finally, the numerical simulations are shown graphically with the software MATLAB.

DYNAMICS OF A PREY-DEPENDENT DIGESTIVE MODEL WITH STATE-DEPENDENT IMPULSIVE CONTROL

2012 ◽  
Vol 22 (04) ◽  
pp. 1250092 ◽  
Author(s):  
LINNING QIAN ◽  
QISHAO LU ◽  
JIARU BAI ◽  
ZHAOSHENG FENG
Keyword(s):  
Numerical Simulations ◽  
Analytical Method ◽  
Impulsive Control ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Period Doubling ◽  
Lambert W Function ◽  
Impulsive Effect ◽  
State Dependent ◽  
Theoretical Results

In this paper, we study the dynamical behavior of a prey-dependent digestive model with a state-dependent impulsive effect. Using the Poincaré map and the Lambert W-function, we find the analytical expression of discrete mapping. Sufficient conditions are established for transcritical bifurcation and period-doubling bifurcation through an analytical method. Exact locations of these bifurcations are explored. Numerical simulations of an example are illustrated which agree well with our theoretical results.

scholarly journals Dynamic Analysis of a Two-Language Competitive Model with Control Strategies

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Lin-Fei Nie ◽  
Zhi-Dong Teng ◽  
Juan J. Nieto ◽  
Il Hyo Jung
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Numerical Simulations ◽  
Control Strategy ◽  
Sufficient Conditions ◽  
Positive Order ◽  
State Dependent ◽  
Competitive Model ◽  
The Impact

The dynamic behavior of a two-language competitive model is analyzed systemically in this paper. By the linearization and the Bendixson-Dulac theorem on dynamical system, some sufficient conditions on the globally asymptotical stability of the trivial equilibria and the existence and the stability of the positive equilibrium of this model are presented. Nextly, in order to protect the endangered language, an optimal control problem relative to this model is explored. We derive some necessary conditions to solve the optimal control problem and present some numerical simulations using a Runge-Kutta fourth-order method. Finally, the languages competitive model is extended to this model assessing the impact of state-dependent pulse control strategy. Using the Poincaré map, differential inequality, and method of qualitative analysis, we prove the existence and stability of positive order-1 periodic solution for this control model. Numerical simulations are carried out to illustrate the main results and the feasibility of state-dependent impulsive control strategy.

scholarly journals Global Stability of Humoral Immunity HIV Infection Models with Chronically Infected Cells and Discrete Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-25
Author(s):  
A. M. Elaiw ◽  
N. A. Alghamdi
Keyword(s):  
Hiv Infection ◽  
Global Stability ◽  
Incidence Rate ◽  
Sufficient Conditions ◽  
Humoral Immune ◽  
Infection Models ◽  
Existence And Stability ◽  
Discrete Delays ◽  
Infected Cells ◽  
Theoretical Results

We study the global stability of three HIV infection models with humoral immune response. We consider two types of infected cells: the first type is the short-lived infected cells and the second one is the long-lived chronically infected cells. In the three HIV infection models, we modeled the incidence rate by bilinear, saturation, and general forms. The models take into account two types of discrete-time delays to describe the time between the virus entering into an uninfected CD4+T cell and the emission of new active viruses. The existence and stability of all equilibria are completely established by two bifurcation parameters,R0andR1. The global asymptotic stability of the steady states has been proven using Lyapunov method. In case of the general incidence rate, we have presented a set of sufficient conditions which guarantee the global stability of model. We have presented an example and performed numerical simulations to confirm our theoretical results.

scholarly journals Mathematical Modelling of Lesser Date Moth Using Sex Pheromone Traps and Natural Enemies

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Moustafa El-Shahed ◽  
Asmaa M. Al-Dubiban
Keyword(s):  
Sex Pheromone ◽  
Date Palm ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Local Bifurcation ◽  
Palm Tree ◽  
Pheromone Traps ◽  
Sex Pheromone Traps ◽  
The Impact ◽  
Theoretical Results

In this paper, a mathematical model for lesser date moth is proposed and analyzed. The interaction between the date palm tree, lesser date moth, and natural enemy has been investigated. The impact of sex pheromone traps on lesser date moth is demonstrated. Some sufficient conditions are obtained to ensure the local and global stability of equilibrium points. The occurrence of local bifurcation near the equilibrium points is performed using Sotomayor’s theorem. Theoretical results are illustrated using numerical simulations.

scholarly journals Dynamics of a stochastic HIV/AIDS model with treatment under regime switching

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Miaomiao Gao ◽  
Daqing Jiang ◽  
Tasawar Hayat ◽  
Ahmed Alsaedi ◽  
Bashir Ahmad
Keyword(s):  
Stationary Distribution ◽  
Regime Switching ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Aids Model ◽  
Telegraph Noise ◽  
Spread Dynamics ◽  
Global Positive Solution ◽  
Theoretical Results ◽  
Hiv Aids

<p style='text-indent:20px;'>This paper focuses on the spread dynamics of an HIV/AIDS model with multiple stages of infection and treatment, which is disturbed by both white noise and telegraph noise. Switching between different environmental states is governed by Markov chain. Firstly, we prove the existence and uniqueness of the global positive solution. Then we investigate the existence of a unique ergodic stationary distribution by constructing suitable Lyapunov functions with regime switching. Furthermore, sufficient conditions for extinction of the disease are derived. The conditions presented for the existence of stationary distribution improve and generalize the previous results. Finally, numerical examples are given to illustrate our theoretical results.</p>

scholarly journals Threshold Analysis and Stationary Distribution of a Stochastic Model with Relapse and Temporary Immunity

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 331 ◽  
Author(s):  
Peng Liu ◽  
Xinzhu Meng ◽  
Haokun Qi
Keyword(s):  
Stochastic Model ◽  
Stationary Distribution ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Markov Semigroup ◽  
Threshold Analysis ◽  
Numerical Examples ◽  
Stochastic Properties ◽  
Symmetric Method ◽  
Temporary Immunity

In this paper, a stochastic model with relapse and temporary immunity is formulated. The main purpose of this model is to investigate the stochastic properties. For two incidence rate terms, we apply the ideas of a symmetric method to obtain the results. First, by constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the extinction and persistence of this system. Then, we investigate the existence of a stationary distribution for this model by employing the theory of an integral Markov semigroup. Finally, the numerical examples are presented to illustrate the analytical findings.

scholarly journals Dynamical Analysis of a Stochastic Multispecies Turbidostat Model

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Yu Mu ◽  
Zuxiong Li ◽  
Huili Xiang ◽  
Hailing Wang
Keyword(s):  
White Noise ◽  
Numerical Simulations ◽  
Dilution Rate ◽  
Stochastic Analysis ◽  
Competitive Exclusion ◽  
Sufficient Conditions ◽  
Dynamical Analysis ◽  
Stochastic Disturbance ◽  
Dynamical Behaviors ◽  
Theoretical Results

A stochastic turbidostat system in which the dilution rate is subject to white noise is investigated in this paper. First of all, sufficient conditions of the competitive exclusion among microorganisms are obtained by employing the techniques of stochastic analysis. Furthermore, the results demonstrate that the competition among microorganisms and stochastic disturbance will affect the dynamical behaviors of microorganisms. Finally, the theoretical results obtained in this contribution are illustrated by numerical simulations.

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