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STABILITY OF STOCHASTIC SIRS MODEL WITH VARIABLE DIFFUSION RATES
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논문 기본 정보

Type
Academic journal
Author
R. Rajaji (University of Madras) M. Pitchaimani (University of Madras) Won Hee Lim (경남대학교)
Journal
경남대학교 기초과학연구소 Nonlinear Functional Analysis and Applications Nonlinear Functional Analysis and Applications Vol.23 No.1 KCI Accredited Journals
Published
2018.3
Pages
31 - 48 (18page)
DOI
10.22771/nfaa.2018.23.01.04

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STABILITY OF STOCHASTIC SIRS MODEL WITH VARIABLE DIFFUSION RATES
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Abstract· Keywords

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In this paper, we extend the classical SIRS epidemic model from a deterministic framework to a stochastic one and formulate it as a stochastic differential equation. We prove the global existence of unique solution. Using the Lyapunov method, we find sufficient conditions for the stochastic asymptotic stability of equilibrium solutions of this model. Finally, establish the existence of a unique ergodic stationary distribution and illustrate our results.
#SIRS model #stochastic asymptotic stability #Lyapunov function.

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References (20)

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L. Arnold / 1974 / Stochastic Differential Equations: Theory and Applications / Wiley google schola V. Capasso / 1978 / A generalization of the Kermack-McKendrick deterministic epidemic model / Math. Biosci 42:41~61 google schola T.C. Gard / 1998 / Introduction to Stochastic Differential Equations / Marcel Dekker google schola H.B. Guo / 2006 / Global stability of the endemic equilibrium of multi-group SIR epidemic models / Can. Appl. Math. Q. 14:259~284 google schola H.W. Hethcote / 1976 / Qualitative analysis of communicable disease models / Math. Biosci 28:335~356 google schola

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