Mean exit time and escape probability for the stochastic logistic growth model with multiplicative α-stable Lévy noise

Tesfay, Almaz; Tesfay, Daniel; Khalaf, Anas D.; Brannan, James R.

doi:10.1142/s0219493721500167

Cited by 12 publications

(19 citation statements)

References 16 publications

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“…For , is a bounded function satisfying on the intervals or . is the independent Poisson random measure on , is the compensated Poisson random measure satisfying , where is a δ -finite measure on a measurable subset of and [ 30 , 34 ]. is mutually independent standard Brownian motion and stands for the intensities of the Gaussian noise [ 35 ].…”

Section: Introductionmentioning

confidence: 99%

“…N(t, dy) is the independent Poisson random measure on R + × R \ {0},N(t, dy) is the compensated Poisson random measure satisfyingN(t, dy) = N(t, dy)π(dy) dt, where π(.) is a δ-finite measure on a measurable subset Y of (0, ∞) and π(Y) < ∞ [30,34]. B j t is mutually independent standard Brownian motion and λ j stands for the intensities of the Gaussian noise [35].…”

Section: Introductionmentioning

confidence: 99%

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Dynamics of a stochastic COVID-19 epidemic model with jump-diffusion

et al. 2021

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For a stochastic COVID-19 model with jump-diffusion, we prove the existence and uniqueness of the global positive solution. We also investigate some conditions for the extinction and persistence of the disease. We calculate the threshold of the stochastic epidemic system which determines the extinction or permanence of the disease at different intensities of the stochastic noises. This threshold is denoted by ξ which depends on white and jump noises. The effects of these noises on the dynamics of the model are studied. The numerical experiments show that the random perturbation introduced in the stochastic model suppresses disease outbreak as compared to its deterministic counterpart. In other words, the impact of the noises on the extinction and persistence is high. When the noise is large or small, our numerical findings show that COVID-19 vanishes from the population if $\xi <1$ ξ < 1 ; whereas the epidemic cannot go out of control if $\xi >1$ ξ > 1 . From this, we observe that white noise and jump noise have a significant effect on the spread of COVID-19 infection, i.e., we can conclude that the stochastic model is more realistic than the deterministic one. Finally, to illustrate this phenomenon, we put some numerical simulations.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamics of a stochastic COVID-19 epidemic model with jump-diffusion

et al. 2021

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“…Recently, the stochastic epidemic models are increasingly investigated by many authors (Zhou and Zhang, 2016;Zhang et al, 2017;Liu et al, 2020;Seraphin Djaoue et al, 2020;Applebaum, 2009;Duan, 2015;Bao and Zhang, 2017;Tilahun et al, 2020;Tesfay et al, 2020) and different methods are adopted for the solution of non-linear systems in integer and fractional order see (Abbasbandy et al, 2017;Arqub, 2019;Joachimiak, 2020;Alchikh and Khuri, 2019;Bougoffa et al, 2016;Djilali, 2019;Djilali, 2018;Djilali, 2020a;Djilali, 2020b;Djilali et al, XXXX;Bentout et al, 2021;Djilali and Ghanbari, 2021). Moreover, moment closure techniques, supported by precise determinacy criteria and evolutive partial differential equations, are as well suitable instruments used in the analysis of similar systems see (Feng and Jin, 2018;Infusino and Kuna, 2020;Infusino et al, 2021;Li et al, 2019;Li and Viglialoro, 2021;Viglialoro and Woolley, 2020).…”

Section: Introductionmentioning

confidence: 99%

A stability analysis on a smoking model with stochastic perturbation

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Kumar

Tesfay

et al. 2021

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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.

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“…Consequently, new results have been established for the proposed estimator of parameter θ that are different from those that have previously been obtained for both fBm and wfBm (see Section 3). On the other hand, we used the most recent results for the numerical simulation (such as in [21][22][23][24]) to discuss the simulation of the sample paths of the mixed weighted fractional Ornstein-Uhlenbeck process.…”

Section: Introductionmentioning

confidence: 99%

A Special Study of the Mixed Weighted Fractional Brownian Motion

et al. 2021

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In this work, we present the analysis of a mixed weighted fractional Brownian motion, defined by ηt:=Bt+ξt, where B is a Brownian motion and ξ is an independent weighted fractional Brownian motion. We also consider the parameter estimation problem for the drift parameter θ>0 in the mixed weighted fractional Ornstein–Uhlenbeck model of the form X0=0;Xt=θXtdt+dηt. Moreover, a simulation is given of sample paths of the mixed weighted fractional Ornstein–Uhlenbeck process.

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Mean exit time and escape probability for the stochastic logistic growth model with multiplicative α-stable Lévy noise

Cited by 12 publications

References 16 publications

Dynamics of a stochastic COVID-19 epidemic model with jump-diffusion

Dynamics of a stochastic COVID-19 epidemic model with jump-diffusion

A stability analysis on a smoking model with stochastic perturbation

A Special Study of the Mixed Weighted Fractional Brownian Motion

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