Exciting chaos with noise: unexpected dynamics in epidemic outbreaks

被引:64
作者
Billings, L [1 ]
Schwartz, IB
机构
[1] Montclair State Univ, Dept Math Sci, Montclair, NJ 07043 USA
[2] USN, Res Lab, Div Plasma Phys, Special Project Nonlinear Sci, Washington, DC 20375 USA
关键词
chaos; noise; bi-instability; population models;
D O I
10.1007/s002850100110
中图分类号
Q [生物科学];
学科分类号
07 ; 0710 ; 09 ;
摘要
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.
引用
收藏
页码:31 / 48
页数:18
相关论文
共 23 条
[1]  
[Anonymous], 1997, CHAOS
[2]  
BILLINGS L, UNPUB INTERMITTENCY
[3]  
Blarer A, 1999, ECOL LETT, V2, P167
[4]  
BOLKER B, 1993, IMA J MATH APPL MED, V10, P83
[5]   CHAOS AND BIOLOGICAL COMPLEXITY IN MEASLES DYNAMICS [J].
BOLKER, BM ;
GRENFELL, BT .
PROCEEDINGS OF THE ROYAL SOCIETY B-BIOLOGICAL SCIENCES, 1993, 251 (1330) :75-81
[6]  
BROOMHEAD D, UNPUB DELAY EMBEDDIN
[7]   Bi-instability and the global role of unstable resonant orbits in a driven laser [J].
Carr, TW ;
Billings, L ;
Schwartz, IB ;
Triandaf, I .
PHYSICA D-NONLINEAR PHENOMENA, 2000, 147 (1-2) :59-82
[8]   FLUCTUATIONS AND THE ONSET OF CHAOS [J].
CRUTCHFIELD, JP ;
HUBERMAN, BA .
PHYSICS LETTERS A, 1980, 77 (06) :407-410
[9]   FLUCTUATIONS AND SIMPLE CHAOTIC DYNAMICS [J].
CRUTCHFIELD, JP ;
FARMER, JD ;
HUBERMAN, BA .
PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS, 1982, 92 (02) :45-82
[10]   A simple model for complex dynamical transitions in epidemics [J].
Earn, DJD ;
Rohani, P ;
Bolker, BM ;
Grenfell, BT .
SCIENCE, 2000, 287 (5453) :667-670