Infinite subharmonic bifurcation in an SEIR epidemic model

Ira B. Schwartz; Hal Smith

doi:10.1007/BF00276090

Infinite subharmonic bifurcation in an SEIR epidemic model

Ira B. Schwartz, Hal Smith

Research output: Contribution to journal › Article › peer-review

194 Scopus citations

Abstract

The existence of both periodic and aperiodic behavior in recurrent epidemics is now well-documented. In this paper, it is proven that for epidemic models that incur permanent immunity with seasonal variations in the contact rate, there exists an infinite number of stable subharmonic solutions. Random effects in the environment could perturb the state of the dynamics from the domain of attraction from one subharmonic to another, thus producing aperiodic levels of incidence.

Original language	English (US)
Pages (from-to)	233-253
Number of pages	21
Journal	Journal Of Mathematical Biology
Volume	18
Issue number	3
DOIs	https://doi.org/10.1007/BF00276090
State	Published - Dec 1 1983

Keywords

Chaos
Epidemic modelling
Infectious diseases
Mathematical modelling
Measles
Subharmonic bifurcation

ASJC Scopus subject areas

Modeling and Simulation
Agricultural and Biological Sciences (miscellaneous)
Applied Mathematics

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10.1007/BF00276090

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author = "Schwartz, {Ira B.} and Hal Smith",

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AU - Smith, Hal

PY - 1983/12/1

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N2 - The existence of both periodic and aperiodic behavior in recurrent epidemics is now well-documented. In this paper, it is proven that for epidemic models that incur permanent immunity with seasonal variations in the contact rate, there exists an infinite number of stable subharmonic solutions. Random effects in the environment could perturb the state of the dynamics from the domain of attraction from one subharmonic to another, thus producing aperiodic levels of incidence.

AB - The existence of both periodic and aperiodic behavior in recurrent epidemics is now well-documented. In this paper, it is proven that for epidemic models that incur permanent immunity with seasonal variations in the contact rate, there exists an infinite number of stable subharmonic solutions. Random effects in the environment could perturb the state of the dynamics from the domain of attraction from one subharmonic to another, thus producing aperiodic levels of incidence.

KW - Chaos

KW - Epidemic modelling

KW - Infectious diseases

KW - Mathematical modelling

KW - Measles

KW - Subharmonic bifurcation

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JF - Journal Of Mathematical Biology

IS - 3

ER -

Infinite subharmonic bifurcation in an SEIR epidemic model

Abstract

Keywords

ASJC Scopus subject areas

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