Sustained oscillations via coherence resonance in SIR

被引：82

作者：

Kuske, Rachel ^{[1
]}

Gordillo, Luis F.

Greenwood, Priscilla

机构：

[1] Univ British Columbia, Dept Math, Vancouver, BC V5Z 1M9, Canada

[2] Arizona State Univ, Dept Math, Tempe, AZ 85287 USA

来源：

JOURNAL OF THEORETICAL BIOLOGY | 2007年 / 245卷 / 03期

基金：

加拿大自然科学与工程研究理事会; 美国国家科学基金会;

关键词：

sustained oscillations; stochastic; SIR; multiple scales; coherence resonance;

D O I：

10.1016/j.jtbi.2006.10.029

中图分类号：

Q [生物科学];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

Sustained oscillations in a stochastic SIR model are studied using a new multiple scale analysis. It captures the interaction of the deterministic and stochastic elements together with the separation of time scales inherent in the appearance of these dynamics. The nearly regular fluctuations in the infected and susceptible populations are described via an explicit construction of a stochastic amplitude equation. The agreement between the power spectral densities of the full model and the approximation verifies that coherence resonance is driving the behavior. The validity criteria for this asymptotic approximation give explicit expressions for the parameter ranges in which one expects to observe this phenomenon. (c) 2006 Elsevier Ltd. All rights reserved.

引用

页码：459 / 469

页数：11

共 30 条

[1] Sustained oscillations in stochastic systems [J].

Aparicio, JP ;

Solari, HG .

MATHEMATICAL BIOSCIENCES, 2001, 169 (01) :15-25

[2]

Arnold L., 1974, STOCHASTIC DIFFERENT, DOI DOI 10.1002/ZAMM.19770570413

[3]

Bailey N. T. J., 1975, The mathematical theory of infectious diseases and its applications, V2nd

[4]

Bartlett M, 1956, P 3 BERK S MATH STAT, V4, P81, DOI DOI 10.2307/2342553

[5]

BRAUER F, 2001, TEXTS APPL MATH, V40

[6] EPIDEMIOLOGICAL MODELS WITH AGE STRUCTURE, PROPORTIONATE MIXING, AND CROSS-IMMUNITY [J].

CASTILLOCHAVEZ, C ;

HETHCOTE, HW ;

ANDREASEN, V ;

LEVIN, SA ;

LIU, WM .

JOURNAL OF MATHEMATICAL BIOLOGY, 1989, 27 (03) :233-258

[7]

Cole J. D, 1996, APPL MATH SCI, V114

[8] Bifurcations of one-dimensional stochastic differential equations [J].

Crauel, H ;

Imkeller, P ;

Steinkamp, M .

STOCHASTIC DYNAMICS, 1999, :27-47

[9] Dynamical resonance can account for seasonality of influenza epidemics [J].

Dushoff, J ;

Plotkin, JB ;

Levin, SA ;

Earn, DJD .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 2004, 101 (48) :16915-16916

[10]

GANG H, 1993, PHYS REV LETT, V71, P807, DOI 10.1103/PhysRevLett.71.807

← 1 2 3 →