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Analysis of a spatially inhomogeneous stochastic partial differential equation epidemic model

Part of: Stochastic analysis Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  16 July 2020

Dang H. Nguyen ,
Nhu N. Nguyen  and
George Yin
Dang H. Nguyen*
Affiliation:
University of Alabama
Nhu N. Nguyen*
Affiliation:
Wayne State University
George Yin*
Affiliation:
Wayne State University
*
*Postal address: University of Alabama, Tuscaloosa, AL35487, USA.
***Postal address: Department of Mathematics, Wayne State University, Detroit, MI, 48202, USA.
***Postal address: Department of Mathematics, Wayne State University, Detroit, MI, 48202, USA.
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Abstract

This work proposes and analyzes a family of spatially inhomogeneous epidemic models. This is our first effort to use stochastic partial differential equations (SPDEs) to model epidemic dynamics with spatial variations and environmental noise. After setting up the problem, the existence and uniqueness of solutions of the underlying SPDEs are examined. Then, definitions of permanence and extinction are given, and certain sufficient conditions are provided for permanence and extinction. Our hope is that this paper will open up windows for investigation of epidemic models from a new angle.

Keywords

SIR modelSPDEmild solutionpositivityextinctionpermanence

MSC classification

Primary: 60H15: Stochastic partial differential equations 92D25: Population dynamics (general) 92D30: Epidemiology
Secondary: 35Q92: PDEs in connection with biology and other natural sciences
Type
Research Papers
Information
Journal of Applied Probability , Volume 57 , Issue 2 , June 2020 , pp. 613 - 636
Copyright
© Applied Probability Trust 2020

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