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    Instabilities and Pattern Formation in Epidemic Spread Induced by Nonlinear Saturation Effects and Ornstein–Uhlenbeck Noise1

    Source: ASME Letters in Dynamic Systems and Control:;2024:;volume( 005 ):;issue: 001::page 11002-1
    Author:
    Singh, Aman Kumar
    ,
    Buschmeyer, Cole
    ,
    Ramakrishnan, Subramanian
    ,
    Kumar, Manish
    DOI: 10.1115/1.4066628
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: We analytically study the emergence of instabilities and the consequent steady-state pattern formation in a stochastic partial differential equation (PDE) based, compartmental model of spatiotemporal epidemic spread. The model is characterized by: (1) strongly nonlinear forces representing the infection transmission mechanism and (2) random environmental forces represented by the Ornstein–Uhlenbeck (O–U) stochastic process which better approximates real-world uncertainties. Employing second-order perturbation analysis and computing the local Lyapunov exponent, we find the emergence of diffusion-induced instabilities and analyze the effects of O–U noise on these instabilities. We obtain a range of values of the diffusion coefficient and correlation time in parameter space that support the onset of instabilities. Notably, the stability and pattern formation results depend critically on the correlation time of the O–U stochastic process; specifically, we obtain lower values of steady-state infection density for higher correlation times. Also, for lower correlation times the results approach those obtained in the white noise case. The analytical results are valid for lower-order correlation times. In summary, the results provide insights into the onset of noise-induced, and Turing-type instabilities in a stochastic PDE epidemic model in the presence of strongly nonlinear deterministic infection forces and stochastic environmental forces represented by Ornstein–Uhlenbeck noise.
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      Instabilities and Pattern Formation in Epidemic Spread Induced by Nonlinear Saturation Effects and Ornstein–Uhlenbeck Noise1

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    http://yetl.yabesh.ir/yetl1/handle/yetl/4305901
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    contributor authorSingh, Aman Kumar
    contributor authorBuschmeyer, Cole
    contributor authorRamakrishnan, Subramanian
    contributor authorKumar, Manish
    date accessioned2025-04-21T10:18:08Z
    date available2025-04-21T10:18:08Z
    date copyright10/11/2024 12:00:00 AM
    date issued2024
    identifier issn2689-6117
    identifier otheraldsc_5_1_011002.pdf
    identifier urihttp://yetl.yabesh.ir/yetl1/handle/yetl/4305901
    description abstractWe analytically study the emergence of instabilities and the consequent steady-state pattern formation in a stochastic partial differential equation (PDE) based, compartmental model of spatiotemporal epidemic spread. The model is characterized by: (1) strongly nonlinear forces representing the infection transmission mechanism and (2) random environmental forces represented by the Ornstein–Uhlenbeck (O–U) stochastic process which better approximates real-world uncertainties. Employing second-order perturbation analysis and computing the local Lyapunov exponent, we find the emergence of diffusion-induced instabilities and analyze the effects of O–U noise on these instabilities. We obtain a range of values of the diffusion coefficient and correlation time in parameter space that support the onset of instabilities. Notably, the stability and pattern formation results depend critically on the correlation time of the O–U stochastic process; specifically, we obtain lower values of steady-state infection density for higher correlation times. Also, for lower correlation times the results approach those obtained in the white noise case. The analytical results are valid for lower-order correlation times. In summary, the results provide insights into the onset of noise-induced, and Turing-type instabilities in a stochastic PDE epidemic model in the presence of strongly nonlinear deterministic infection forces and stochastic environmental forces represented by Ornstein–Uhlenbeck noise.
    publisherThe American Society of Mechanical Engineers (ASME)
    titleInstabilities and Pattern Formation in Epidemic Spread Induced by Nonlinear Saturation Effects and Ornstein–Uhlenbeck Noise1
    typeJournal Paper
    journal volume5
    journal issue1
    journal titleASME Letters in Dynamic Systems and Control
    identifier doi10.1115/1.4066628
    journal fristpage11002-1
    journal lastpage11002-6
    page6
    treeASME Letters in Dynamic Systems and Control:;2024:;volume( 005 ):;issue: 001
    contenttypeFulltext
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    نرم افزار کتابخانه دیجیتال "دی اسپیس" فارسی شده توسط یابش برای کتابخانه های ایرانی | تماس با یابش
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