Subharmonic bifurcation in an S-I-R epidemic model

Hal Smith

doi:10.1007/BF00305757

Subharmonic bifurcation in an S-I-R epidemic model

Hal Smith

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

67 Scopus citations

Abstract

An S → I → R epidemic model with annual oscillation in the contact rate is analyzed for the existence of subharmonic solutions of period two years. We prove that a stable period two solution bifurcates from a period one solution as the amplitude of oscillation in the contact rate exceeds a threshold value. This makes rigorous earlier formal arguments of Z. Grossman, I. Gumowski, and K. Dietz [4].

Original language	English (US)
Pages (from-to)	163-177
Number of pages	15
Journal	Journal Of Mathematical Biology
Volume	17
Issue number	2
DOIs	https://doi.org/10.1007/BF00305757
State	Published - Jun 1 1983

Keywords

Bifurcation
Epidemic model
Subharmonic solution

ASJC Scopus subject areas

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

Access to Document

10.1007/BF00305757

Cite this

@article{970ad1a2c606435bbe66d2a2dac38369,

title = "Subharmonic bifurcation in an S-I-R epidemic model",

abstract = "An S → I → R epidemic model with annual oscillation in the contact rate is analyzed for the existence of subharmonic solutions of period two years. We prove that a stable period two solution bifurcates from a period one solution as the amplitude of oscillation in the contact rate exceeds a threshold value. This makes rigorous earlier formal arguments of Z. Grossman, I. Gumowski, and K. Dietz [4].",

keywords = "Bifurcation, Epidemic model, Subharmonic solution",

author = "Hal Smith",

year = "1983",

month = jun,

day = "1",

doi = "10.1007/BF00305757",

language = "English (US)",

volume = "17",

pages = "163--177",

journal = "Journal Of Mathematical Biology",

issn = "0303-6812",

publisher = "Springer Verlag",

number = "2",

}

TY - JOUR

T1 - Subharmonic bifurcation in an S-I-R epidemic model

AU - Smith, Hal

PY - 1983/6/1

Y1 - 1983/6/1

N2 - An S → I → R epidemic model with annual oscillation in the contact rate is analyzed for the existence of subharmonic solutions of period two years. We prove that a stable period two solution bifurcates from a period one solution as the amplitude of oscillation in the contact rate exceeds a threshold value. This makes rigorous earlier formal arguments of Z. Grossman, I. Gumowski, and K. Dietz [4].

AB - An S → I → R epidemic model with annual oscillation in the contact rate is analyzed for the existence of subharmonic solutions of period two years. We prove that a stable period two solution bifurcates from a period one solution as the amplitude of oscillation in the contact rate exceeds a threshold value. This makes rigorous earlier formal arguments of Z. Grossman, I. Gumowski, and K. Dietz [4].

KW - Bifurcation

KW - Epidemic model

KW - Subharmonic solution

UR - http://www.scopus.com/inward/record.url?scp=0020963836&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0020963836&partnerID=8YFLogxK

U2 - 10.1007/BF00305757

DO - 10.1007/BF00305757

M3 - Article

C2 - 6886569

AN - SCOPUS:0020963836

SN - 0303-6812

VL - 17

SP - 163

EP - 177

JO - Journal Of Mathematical Biology

JF - Journal Of Mathematical Biology

IS - 2

ER -

Subharmonic bifurcation in an S-I-R epidemic model

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this