scholarly journals Threshold Dynamics of a Non-Linear Stochastic Viral Model with Time Delay and CTL Responsiveness

Life ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 766
Author(s):  
Jianguo Sun ◽  
Miaomiao Gao ◽  
Daqing Jiang
Keyword(s):  
Numerical Simulation ◽  
Time Delay ◽  
Lyapunov Function ◽  
Viral Infection ◽  
Positive Solution ◽  
Existence And Uniqueness ◽  
Distributed Delay ◽  
Viral Disease ◽  
Threshold Dynamics ◽  
Global Positive Solution

This article focuses on a stochastic viral model with distributed delay and CTL responsiveness. It is shown that the viral disease will be extinct if the stochastic reproductive ratio is less than one. However, when the stochastic reproductive ratio is more than one, the viral infection system consists of an ergodic stationary distribution. Furthermore, we obtain the existence and uniqueness of the global positive solution by constructing a suitable Lyapunov function. Finally, we illustrate our results by numerical simulation.

Dynamics of a stochastic rabies epidemic model with markovian switching

2021 ◽  
pp. 2150032
Author(s):  
Hao Peng ◽  
Xinhong Zhang ◽  
Daqing Jiang
Keyword(s):  
Lyapunov Function ◽  
White Noise ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Epidemic Model ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Telegraph Noise ◽  
Global Positive Solution ◽  
Theoretical Results

In this paper, we analyze a stochastic rabies epidemic model which is perturbed by both white noise and telegraph noise. First, we prove the existence of the unique global positive solution. Second, by constructing an appropriate Lyapunov function, we establish a sufficient condition for the existence of a unique ergodic stationary distribution of the positive solutions to the model. Then we establish sufficient conditions for the extinction of diseases. Finally, numerical simulations are introduced to illustrate our theoretical results.

scholarly journals Dynamical Behavior of a Stochastic SIRC Model for Influenza A

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 745 ◽  
Author(s):  
Tongqian Zhang ◽  
Tingting Ding ◽  
Ning Gao ◽  
Yi Song
Keyword(s):  
Lyapunov Function ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Epidemic Model ◽  
Influenza A ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Global Positive Solution ◽  
Theoretical Results ◽  
Stochastic Lyapunov Function

In this paper, a stochastic SIRC epidemic model for Influenza A is proposed and investigated. First, we prove that the system exists a unique global positive solution. Second, the extinction of the disease is explored and the sufficient conditions for extinction of the disease are derived. And then the existence of a unique ergodic stationary distribution of the positive solutions for the system is discussed by constructing stochastic Lyapunov function. Furthermore, numerical simulations are employed to illustrate the theoretical results. Finally, we give some further discussions about the system.

scholarly journals Stationary distribution of a stochastic SIRD epidemic model of Ebola with double saturated incidence rates and vaccination

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Panpan Wang ◽  
Jianwen Jia
Keyword(s):  
Stochastic Model ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Stationary Distribution ◽  
Epidemic Model ◽  
Existence And Uniqueness ◽  
Lyapunov Functions ◽  
Incidence Rates ◽  
Saturated Incidence ◽  
Global Positive Solution

Abstract In this paper, a stochastic SIRD model of Ebola with double saturated incidence rates and vaccination is considered. Firstly, the existence and uniqueness of a global positive solution are obtained. Secondly, by constructing suitable Lyapunov functions and using Khasminskii’s theory, we show that the stochastic model has a unique stationary distribution. Moreover, the extinction of the disease is also analyzed. Finally, numerical simulations are carried out to portray the analytical results.

scholarly journals Stochastically Ultimate Boundedness and Global Attraction of Positive Solution for a Stochastic Competitive System

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Shengliang Guo ◽  
Zhijun Liu ◽  
Huili Xiang
Keyword(s):  
Lyapunov Function ◽  
Positive Solution ◽  
Finite Time ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Ultimate Boundedness ◽  
Competitive System ◽  
Global Attraction ◽  
Stochastically Ultimate Boundedness ◽  
Theoretical Results

A stochastic competitive system is investigated. We first show that the positive solution of the above system does not explode to infinity in a finite time, and the existence and uniqueness of positive solution are discussed. Later, sufficient conditions for the stochastically ultimate boundedness of positive solution are derived. Also, with the help of Lyapunov function, sufficient conditions for the global attraction of positive solution are established. Finally, numerical simulations are presented to justify our theoretical results.

scholarly journals Asymptotic Behaviors for Delay Lotka–Volterra Model Disturbed by G-Brownian Motion

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Ping He ◽  
Yong Ren ◽  
Defei Zhang
Keyword(s):  
Brownian Motion ◽  
Positive Solution ◽  
Finite Time ◽  
Existence And Uniqueness ◽  
Volterra Model ◽  
Natural Assumption ◽  
Asymptotic Behaviors ◽  
Global Positive Solution

In this paper, we propose the stochastic Lotka–Volterra model with delay disturbed by G-Brownian motion dx=diagx1,x2,…,xnAxt−τ+bdBt+σxdBt. Under a natural assumption on noise, we study existence and uniqueness of the global positive solution for the system and its asymptotic pathwise moment behavior and prove that the solution does not explode to infinity in a finite time.

scholarly journals Dynamics of a Stochastic Three-Species Food Web Model with Omnivory and Ratio-Dependent Functional Response

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-19
Author(s):  
Guirong Liu ◽  
Rong Liu
Keyword(s):  
Lyapunov Function ◽  
Numerical Simulations ◽  
Food Web ◽  
Positive Solution ◽  
Sufficient Conditions ◽  
Stochastic Comparison ◽  
Top Predator ◽  
Global Positive Solution ◽  
Persistent In Mean ◽  
Food Web Model

This paper is concerned with a stochastic three-species food web model with omnivory which is defined as feeding on more than one trophic level. The model involves a prey, an intermediate predator, and an omnivorous top predator. First, by the stochastic comparison theorem, we show that there is a unique global positive solution to the model. Next, we investigate the asymptotic pathwise behavior of the model. Then, we conclude that the model is persistent in mean and extinct and discuss the stochastic persistence of the model. Further, by constructing a suitable Lyapunov function, we establish sufficient conditions for the existence of an ergodic stationary distribution to the model. Then, we present the application of the main results in some special models. Finally, we introduce some numerical simulations to support the main results obtained. The results in this paper generalize and improve the previous related results.

scholarly journals Relaxation Oscillations and Dynamical Properties in Two Time-Delay Slow-Fast Modified Leslie-Gower Models

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Yufeng Wang ◽  
Youhua Qian ◽  
Bingwen Lin
Keyword(s):  
Numerical Simulation ◽  
Perturbation Theory ◽  
Time Delay ◽  
Existence And Uniqueness ◽  
Relaxation Oscillation ◽  
Singular Perturbation Theory ◽  
Geometric Singular Perturbation Theory ◽  
Relaxation Oscillations ◽  
Oscillation Cycle ◽  
Dynamical Properties

In this paper, we consider two kinds of time-delay slow-fast modified Leslie-Gower models. For the first system, we prove the existence and uniqueness of relaxation oscillation cycle through the geometric singular perturbation theory and entry-exit function. For the second system, we put forward a conjecture that the relaxation oscillation of the system is unique. Numerical simulation also verifies our results for the systems.

scholarly journals Dynamical Analysis of Two-Microorganism and Single Nutrient Stochastic Chemostat Model with Monod-Haldane Response Function

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Mengnan Chi ◽  
Wencai Zhao
Keyword(s):  
Lyapunov Function ◽  
Response Function ◽  
Existence And Uniqueness ◽  
Random Perturbation ◽  
Equilibrium Points ◽  
Dynamical Analysis ◽  
Deterministic System ◽  
Chemostat Model ◽  
Global Positive Solution ◽  
The Stability

In this paper, we formulate and investigate a two-microorganism and single nutrient chemostat model with Monod-Haldane response function and random perturbation. First, for the corresponding deterministic system, we introduce the conditions of the stability of the equilibrium points. Then, using Lyapunov function and Itô’s formula, we investigate the existence and uniqueness of the global positive solution of the stochastic chemostat model. Furthermore, we explore and obtain the criterions of the extinction and the permanence for the stochastic model. Finally, numerical simulations are carried out to illustrate our main results.

Modern aspects of tactics in the genital herpes viral infection (literature review)

GYNECOLOGY ◽  
2018 ◽  
Vol 20 (2) ◽  
pp. 67-73
Author(s):  
T Yu Pestrikova ◽  
E A Yurasova ◽  
I V Yurasov ◽  
A V Kotelnikova
Keyword(s):  
Literature Review ◽  
Viral Infection ◽  
Genital Herpes ◽  
Fetal Death ◽  
Malignant Tumors ◽  
Adult Population ◽  
Viral Disease ◽  
Intrauterine Fetal Death ◽  
Complicated Course ◽  
Simplex Virus

Genital herpes affects all population groups. 98% of the adult population worldwide have antibodies to the herpes simplex virus (HSV-1 or 2). This viral infection is a significant medical and social problem. HSV can lead to a complicated course of pregnancy, causing miscarriages, premature birth, intrauterine fetal death, systemic viral disease in newborns. There is evidence that HSV has a connection with malignant tumors of the prostate and cervix, contributing to their development. This literature review contains modern aspects of epidemiology, etiology, pathogenesis, clinic, diagnosis, treatment of genital herpes, including its recurring forms with valacyclovir (Valvir). Indications for hospitalization of patients with genital herpes were noted and the prognosis of this pathology was determined. The tactics of managing pregnant women with this pathology is presented.

Global stability analysis of fractional-order gene regulatory networks with time delay

2019 ◽  
Vol 12 (06) ◽  
pp. 1950067 ◽  
Author(s):  
Zhaohua Wu ◽  
Zhiming Wang ◽  
Tiejun Zhou
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Gene Regulatory Networks ◽  
Existence And Uniqueness ◽  
Regulatory Networks ◽  
Lyapunov Method ◽  
Regulation Mechanism ◽  
Global Stability Analysis ◽  
Gene Regulatory ◽  
The Stability

Fractional-order gene regulatory networks with time delay (DFGRNs) have proven that they are more suitable to model gene regulation mechanism than integer-order. In this paper, a novel DFGRN is proposed. The existence and uniqueness of the equilibrium point for the DFGRN are proved under certain conditions. On this basis, the conditions on the global asymptotic stability are established by using the Lyapunov method and comparison theorem for the DFGRN, and the stability conditions are dependent on the fractional-order [Formula: see text]. Finally, numerical simulations show that the obtained results are reasonable.

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