Exciting chaos with noise: Unexpected dynamics in epidemic outbreaks

Lora Billings, I. B. Schwartz

Research output: Contribution to journalArticle

54 Citations (Scopus)

Abstract

In this paper, we identify a mechanism for chaos in the presence of noise. In a study of the SEIR model, which predicts epidemic outbreaks in childhood diseases, we show how chaotic dynamics can be attained by adding stochastic perturbations at parameters where chaos does not exist apriori. Data recordings of epidemics in childhood diseases are still argued as deterministic chaos. There also exists noise due to uncertainties in the contact parameters between those who are susceptible and those who are infected, as well as random fluctuations in the population. Although chaos has been found in deterministic models, it only occurs in parameter regions that require a very large population base or other large seasonal forcing. Our work identifies the mechanism whereby chaos can be induced by noise for realistic parameter regions of the deterministic model where it does not naturally occur.

Original languageEnglish
Pages (from-to)31-48
Number of pages18
JournalJournal of Mathematical Biology
Volume44
Issue number1
DOIs
StatePublished - 1 Jan 2002

Fingerprint

Chaos theory
Disease Outbreaks
Noise
Chaos
childhood
Deterministic Model
Deterministic Chaos
Stochastic Perturbation
Population
Uncertainty
Chaotic Dynamics
uncertainty
Data recording
Forcing
Contact
Fluctuations
Predict
Model

Keywords

  • Bi-instability
  • Chaos
  • Noise
  • Population models

Cite this

@article{4c5a6e0b413f46da8248c250d94610fa,
title = "Exciting chaos with noise: Unexpected dynamics in epidemic outbreaks",
abstract = "In this paper, we identify a mechanism for chaos in the presence of noise. In a study of the SEIR model, which predicts epidemic outbreaks in childhood diseases, we show how chaotic dynamics can be attained by adding stochastic perturbations at parameters where chaos does not exist apriori. Data recordings of epidemics in childhood diseases are still argued as deterministic chaos. There also exists noise due to uncertainties in the contact parameters between those who are susceptible and those who are infected, as well as random fluctuations in the population. Although chaos has been found in deterministic models, it only occurs in parameter regions that require a very large population base or other large seasonal forcing. Our work identifies the mechanism whereby chaos can be induced by noise for realistic parameter regions of the deterministic model where it does not naturally occur.",
keywords = "Bi-instability, Chaos, Noise, Population models",
author = "Lora Billings and Schwartz, {I. B.}",
year = "2002",
month = "1",
day = "1",
doi = "10.1007/s002850100110",
language = "English",
volume = "44",
pages = "31--48",
journal = "Journal of Mathematical Biology",
issn = "0303-6812",
publisher = "Springer Verlag",
number = "1",

}

Exciting chaos with noise : Unexpected dynamics in epidemic outbreaks. / Billings, Lora; Schwartz, I. B.

In: Journal of Mathematical Biology, Vol. 44, No. 1, 01.01.2002, p. 31-48.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Exciting chaos with noise

T2 - Unexpected dynamics in epidemic outbreaks

AU - Billings, Lora

AU - Schwartz, I. B.

PY - 2002/1/1

Y1 - 2002/1/1

N2 - In this paper, we identify a mechanism for chaos in the presence of noise. In a study of the SEIR model, which predicts epidemic outbreaks in childhood diseases, we show how chaotic dynamics can be attained by adding stochastic perturbations at parameters where chaos does not exist apriori. Data recordings of epidemics in childhood diseases are still argued as deterministic chaos. There also exists noise due to uncertainties in the contact parameters between those who are susceptible and those who are infected, as well as random fluctuations in the population. Although chaos has been found in deterministic models, it only occurs in parameter regions that require a very large population base or other large seasonal forcing. Our work identifies the mechanism whereby chaos can be induced by noise for realistic parameter regions of the deterministic model where it does not naturally occur.

AB - In this paper, we identify a mechanism for chaos in the presence of noise. In a study of the SEIR model, which predicts epidemic outbreaks in childhood diseases, we show how chaotic dynamics can be attained by adding stochastic perturbations at parameters where chaos does not exist apriori. Data recordings of epidemics in childhood diseases are still argued as deterministic chaos. There also exists noise due to uncertainties in the contact parameters between those who are susceptible and those who are infected, as well as random fluctuations in the population. Although chaos has been found in deterministic models, it only occurs in parameter regions that require a very large population base or other large seasonal forcing. Our work identifies the mechanism whereby chaos can be induced by noise for realistic parameter regions of the deterministic model where it does not naturally occur.

KW - Bi-instability

KW - Chaos

KW - Noise

KW - Population models

UR - http://www.scopus.com/inward/record.url?scp=0036369855&partnerID=8YFLogxK

U2 - 10.1007/s002850100110

DO - 10.1007/s002850100110

M3 - Article

C2 - 11942524

AN - SCOPUS:0036369855

VL - 44

SP - 31

EP - 48

JO - Journal of Mathematical Biology

JF - Journal of Mathematical Biology

SN - 0303-6812

IS - 1

ER -