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Comparative Study
. 1983;17(2):163-77.
doi: 10.1007/BF00305757.

Subharmonic bifurcation in an S-I-R epidemic model

H L Smith
Comparative Study

Subharmonic bifurcation in an S-I-R epidemic model

H L Smith. J Math Biol. 1983.

Abstract

An S leads to I leads to 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].

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References

    1. Am J Epidemiol. 1973 Dec;98(6):453-68 - PubMed
    1. J Math Biol. 1983;17(2):179-90 - PubMed
    1. Theor Popul Biol. 1980 Oct;18(2):204-43 - PubMed

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