State transitions in the Morris-Lecar model under stable Lévy noise

Cai, Rui; Liu, Yancai; Duan, Jinqiao; Abebe, Almaz Tesfay

doi:10.48550/arxiv.1906.07613

Cited by 1 publication

(1 citation statement)

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“…Up to now, many results on stochastic epidemic models have been investigated. Articles [9][10][11][12][13][14][15][16][17] have studied stochastic epidemic models influenced by Lévy noise. Motivated from the above researches, we assume that the contact rate is perturbed by Lévy noise.…”

Section: Introductionmentioning

confidence: 99%

Stochastic COVID-19 Model Influenced by Non-Gaussian Noise

Tesfay¹,

Zeb²,

Chu³

et al. 2021

Preprint

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Natural changes have been played a vital part within the consider of irresistible illnesses uncommonly coronavirus. It is important to think about the effect of irregular unsettling influence on epidemic models. In this work, first we present a SIR coronavirus mathematical model and consider that the contact rate is perturbed by Lévy noise. To protect and control diseases, the Lévy process should be used. Then, we discuss the dynamics of the deterministic model and for the global positive solution of the stochastic model, present the existence and uniqueness. Further, explore a few conditions for the termination and persistence of the infection. Then derive the basic reproduction number that determines the extinction and the persistence of the disease (infection). When the noise is huge or little, the numerical results appear that the COVID19 vanishes from the individuals on the chance that the reproduction number is less than one; though control the epidemic illnesses in the event that reproduction number is greater than one. Finally, for the demonstration of this phenomenon numerical simulations are presented.

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