A stability analysis on a smoking model with stochastic perturbation

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Anwar Zeb ◽  
Sunil Kumar ◽  
Almaz Tesfay ◽  
Anil Kumar
Keyword(s):  
Stochastic Model ◽  
Stochastic System ◽  
Existence And Uniqueness ◽  
Deterministic Model ◽  
Sufficient Conditions ◽  
Reproductive Number ◽  
Content Type ◽  
Model Form ◽  
The World ◽  
Dynamic Stochastic

Purpose The purpose of this paper is to investigate the effects of irregular unsettling on the smoking model in form of the stochastic model as in the deterministic model these effects are neglected for simplicity. Design/methodology/approach In this research, the authors investigate a stochastic smoking system in which the contact rate is perturbed by Lévy noise to control the trend of smoking. First, present the formulation of the stochastic model and study the dynamics of the deterministic model. Then the global positive solution of the stochastic system is discussed. Further, extinction and the persistence of the proposed system are presented on the base of the reproductive number. Findings The authors discuss the dynamics of the deterministic smoking model form and further present the existence and uniqueness of non-negative global solutions for the stochastic system. Some previous study’s mentioned in the Introduction can be improved with the help of obtaining results, graphically present in this manuscript. In this regard, the authors present the sufficient conditions for the extinction of smoking for reproductive number is less than 1. Research limitations/implications In this work, the authors investigated the dynamic stochastic smoking model with non-Gaussian noise. The authors discussed the dynamics of the deterministic smoking model form and further showed for the stochastic system the existence and uniqueness of the non-negative global solution. Some previous study’s mentioned in the Introduction can be improved with the help of obtained results, clearly shown graphically in this manuscript. In this regard, the authors presented the sufficient conditions for the extinction of smoking, if <1, which can help in the control of smoking. Motivated from this research soon, the authors will extent the results to propose new mathematical models for the smoking epidemic in the form of fractional stochastic modeling. Especially, will investigate the effective strategies for control smoking throughout the world. Originality/value This study is helpful in the control of smoking throughout the world.

Stochastic dynamics for the solutions of a modified Holling–Tanner model with random perturbation

2014 ◽  
Vol 25 (11) ◽  
pp. 1450105 ◽  
Author(s):  
Zhenjie Liu
Keyword(s):  
Stochastic System ◽  
Stochastic Dynamics ◽  
Deterministic Model ◽  
Random Perturbation ◽  
Sufficient Conditions ◽  
Unique Positive Solution ◽  
Initial Value ◽  
Environmental Forcing ◽  
Predator Prey ◽  
Predator Prey Model

In this paper, we consider a stochastic nonautonomous predator–prey model with modified Leslie–Gower and Holling II schemes in the presence of environmental forcing. The deterministic model is the modified Holling–Tanner model which is an extension of the classical Leslie–Gower model. We show that there is a unique positive solution to the stochastic system for any positive initial value. Sufficient conditions for strong persistence in mean and extinction to the stochastic system are established.

scholarly journals Analysis of the stochastic model for predicting the novel coronavirus disease

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ndolane Sene
Keyword(s):  
Stochastic Model ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
The Novel ◽  
Stochastic Perturbations ◽  
Numerical Investigations ◽  
Rapid Spread ◽  
The World ◽  
Novel Coronavirus

Abstract In this paper, we propose a mathematical model to predict the novel coronavirus. Due to the rapid spread of the novel coronavirus disease in the world, we add to the deterministic model of the coronavirus the terms of the stochastic perturbations. In other words, we consider in this paper a stochastic model to predict the novel coronavirus. The equilibrium points of the deterministic model have been determined, and the reproduction number of our deterministic model has been implemented. The asymptotic behaviors of the solutions of the stochastic model around the equilibrium points have been studied. The numerical investigations and the graphical representations obtained with the novel stochastic model are made using the classical stochastic numerical scheme.

How do the financial and oil sanctions affect the Iran's economy: a DSGE framework

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Seyyed Reza Nakhli ◽  
Monireh Rafat ◽  
Rasul Bakhshi Dastjerdi ◽  
Meysam Rafei
Keyword(s):  
Open Economy ◽  
Economic Effect ◽  
Current Paper ◽  
Dsge Models ◽  
Dsge Model ◽  
Content Type ◽  
Macroeconomic Variables ◽  
The World ◽  
Dynamic Stochastic ◽  
The Government

PurposeThe purpose of the current paper is to analyze the simultaneous effects of oil sanctions and financial sanctions on Iran's macroeconomic variables in a small open economy in the dynamic stochastic general equilibrium (DSGE) framework.Design/methodology/approachA DSGE model with the new Keynesian approach has been designed for the above mentioned purpose giving consideration to households, production, trade, oil, government and central bank sectors. All of the parameters were calibrated by using geometric means of macroeconomic variables in 2004–2017 as the steady-state values of the variables in the static model.FindingsAmplifying the intensity of the oil sanctions reduces oil production due to decreasing investment, technology and export of oil and reduces the central bank's foreign reserves ratio to the money base that leads to an increasing exchange rate. Furthermore, oil sanctions decrease the government revenues due to a decrease in oil export and by the government imposing an expansionary fiscal policy in the form of increasing current expenditure and preserving construction expenditure to prevent deepening the recession, which causes budget deficit and then the issue of more bonds with a higher nominal interest rate. On the other hand, financial sanctions raise transaction costs and marginal costs in the trade sectors that lead to inflation and a decrease in nonoil export and various kinds of imports. Due to inflation and uncertainty, consumption of a household increases and investment expenditure of a household decreases.Originality/valueTo the best of the author's knowledge, few studies in the world have analyzed the economic effect of the sanctions in the framework of DSGE models. There is no study in Iran to date which investigates the effects of the sanctions in the form of a DSGE model. So, this paper is the first study in Iran and one of the few studies in the world using a DSGE model for analyzing the effects of sanctions. Imposing three kinds of oil sanctions in addition to a financial sanction is another innovation of the current paper.

scholarly journals Stochastic SIRC epidemic model with time-delay for COVID-19

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
F. A. Rihan ◽  
H. J. Alsakaji ◽  
C. Rajivganthi
Keyword(s):  
Time Delay ◽  
White Noise ◽  
Existence And Uniqueness ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Sufficient Conditions ◽  
Stochastic Epidemic ◽  
Feedback Time ◽  
Precipitation And Temperature ◽  
Stochastic Lyapunov Function

Abstract Environmental factors, such as humidity, precipitation, and temperature, have significant impacts on the spread of the new strain coronavirus COVID-19 to humans. In this paper, we use a stochastic epidemic SIRC model, with cross-immune class and time-delay in transmission terms, for the spread of COVID-19. We analyze the model and prove the existence and uniqueness of positive global solution. We deduce the basic reproduction number ${\mathcal{R}}_{0}^{s}$ R 0 s for the stochastic model which is smaller than ${\mathcal{R}}_{0}$ R 0 of the corresponding deterministic model. Sufficient conditions that guarantee the existence of a unique ergodic stationary distribution, using the stochastic Lyapunov function, and conditions for the extinction of the disease are obtained. Our findings show that white noise plays an important part in controlling the spread of the disease; When the white noise is relatively large, the infectious diseases will become extinct; Re-infection and periodic outbreaks can occur due to the existence of feedback time-delay (or memory) in the transmission terms.

Dynamics of delayed stochastic predator–prey models with feedback controls based on discrete observations

2017 ◽  
Vol 10 (03) ◽  
pp. 1750040 ◽  
Author(s):  
Dianli Zhao ◽  
Sanling Yuan
Keyword(s):  
Numerical Simulations ◽  
Stochastic System ◽  
Necessary Conditions ◽  
Deterministic Model ◽  
Sufficient Conditions ◽  
Discrete Observations ◽  
Feedback Controls ◽  
Predator Prey ◽  
Global Positive Solution ◽  
Predator Prey Models

In this paper, we concern a class of the generalized delayed stochastic predator–prey models with feedback controls based on discrete observations. The existence of global positive solution is given first. Then we discuss the deterministic model briefly, and establish the necessary conditions and the sufficient conditions for almost-sure extinction and persistence in mean for the stochastic system, where we show that the feedback controls can change the properties of the population systems significantly. Finally, numerical simulations are introduced to support the main results.

scholarly journals A Stochastic Turbidostat Model With Ornstein-Uhlenbeck Process: Dynamics Analysis and Numerical Simulations

2021 ◽  
Author(s):  
Daqing Jiang ◽  
Xiaojie Mu ◽  
Tasawar Hayat ◽  
Ahmed Alsaedi
Keyword(s):  
Stationary Distribution ◽  
Existence And Uniqueness ◽  
Deterministic Model ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Positive Equilibrium ◽  
Uhlenbeck Process ◽  
Process Dynamics ◽  
Ornstein Uhlenbeck Process ◽  
Long Term Behavior

Abstract Many turbidostat models are affected by environmental noise due to various complicated and uncertain factors, and Ornstein-Uhlenbeck process is a more effective and precise way. We formulate a stochastic turbidostat system incorporating Ornstein-Uhlenbeck process in this paper, develop dynamical behavior for the stochastic model, which include the existence and uniqueness of globally positive equilibrium, sufficient conditions of the extinction, the existence of a unique stationary distribution and an expression of density function of quasi-stationary distribution around the positive solution of the deterministic model. The results indicate that the weaker volatility intensity canensure the existence and uniqueness of stationary distribution, and the stronger reversion speed can lead to the extinction of microorganism. The validity of analytical results is verified through numerical simulation, which assess the influence of the reversion speed and the volatility intensity on the long-term behavior of microorganism.

ANALYSIS OF A STOCHASTIC HBV INFECTION MODEL WITH NONLINEAR INCIDENCE RATE

2019 ◽  
Vol 27 (03) ◽  
pp. 399-421 ◽  
Author(s):  
HONGWEN HUI ◽  
LIN-FEI NIE
Keyword(s):  
Numerical Simulations ◽  
Deterministic Model ◽  
Sufficient Conditions ◽  
Stochastic Perturbation ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Infection Model ◽  
Exponentially Stable ◽  
Infected Cells ◽  
Theoretical Results

Considering that environmental factors, diet, subconscious mind and other uncertainties play an important role in the process of delaying and treating diseases, we propose, in this paper, an amended Hepatitis B virus (HBV) model with stochastic perturbation, and investigate the longtime dynamics of this stochastic model. First, if the basic reproductive number of the corresponding deterministic model is less than 1, some sufficient conditions for almost surely exponentially stable in the sense of the infected cells and free virus are established, and the stationary probability density function of the uninfected sell is also obtained. Further, some sufficient conditions for the existence of the stationary distribution are obtained for the basic reproductive number more than 1. In addition, oscillatory behaviors of this model about the equilibrium of the corresponding deterministic model are discussed. Finally, numerical simulations demonstrate the main theoretical results and show stochastic virus model has more dynamic behaviors relative to its corresponding deterministic model. Theoretical results and numerical simulations imply that the intensity and “type (divided into positive and negative)” of white noise play very important roles in the treatment of infectious disease, which can make the disease more and more repetitive and unpredictable. Of course, comfortable environment, reasonable diet, optimistic mood and other positive uncertainty factors have active effects on the treatment and delaying of diseases, but not the converse.

scholarly journals Correlated Stochastic Epidemic Model for the Dynamics of SARS-CoV-2 with Vaccination

2021 ◽  
Author(s):  
Tahir Khan ◽  
Roman Ullah ◽  
Gul Zaman ◽  
Youssef Khatib
Keyword(s):  
Mathematical Model ◽  
Brownian Motion ◽  
Stochastic Model ◽  
Existence And Uniqueness ◽  
Human Population ◽  
Sufficient Conditions ◽  
Stochastic Epidemic ◽  
Stochastic Epidemic Model ◽  
Virus Spreading ◽  
Theoretical Results

Abstract We formulate a mathematical model has been proposed to describe the stochastic influence of SARS-CoV-2 virus with various sources of randomness and vaccination. We assume the various sources of ran-domness in each population groups by different Brownian motion. We develop the correlated stochastic model by taking into account the various sources of randomness by different Brownian motions and distributed the total human population in three groups of susceptible, infected and recovered with reservoir class. Because reservoir play a significant role in the transmission of SARS-CoV-2 virus spreading. Moreover, the vaccination of susceptible are also accorded. Once we formulate the correlated stochastic model, the existence and uniqueness of positive solution will be discussed to show the problem feasibility. The SARS-CoV-2 extinction as well as persistency will be also discussed and we will obtain the sufficient conditions for it. At the last all the theoretical results will be supported via numerical/graphical findings.

scholarly journals Analysis on a Stochastic Predator-Prey Model with Modified Leslie-Gower Response

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Jingliang Lv ◽  
Ke Wang
Keyword(s):  
Global Existence ◽  
Stochastic Model ◽  
Unique Solution ◽  
Stochastic System ◽  
Finite Time ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

This paper presents an investigation of asymptotic properties of a stochastic predator-prey model with modified Leslie-Gower response. We obtain the global existence of positive unique solution of the stochastic model. That is, the solution of the system is positive and not to explode to infinity in a finite time. And we show some asymptotic properties of the stochastic system. Moreover, the sufficient conditions for persistence in mean and extinction are obtained. Finally we work out some figures to illustrate our main results.

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