Journal of Mathematical Biology

, Volume 44, Issue 1, pp 31–48

Exciting chaos with noise: unexpected dynamics in epidemic outbreaks

  • L. Billings
  • I. B. Schwartz

DOI: 10.1007/s002850100110

Cite this article as:
Billings, L. & Schwartz, I. J Math Biol (2002) 44: 31. doi:10.1007/s002850100110


 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.

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • L. Billings
    • 1
  • I. B. Schwartz
    • 2
  1. 1.Department of Mathematical Sciences, Montclair State University, Upper Montclair, NJ 07043, USA. e-mail: billingsl@mail.montclair.eduUS
  2. 2.Naval Research Laboratory, Special Project in Nonlinear Science, Plasma Physics Division, Code 6700.3, Washington, DC 20375, USA. Contact: I.B. Schwartz, e-mail: