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) |
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Pages (from-to) | 163-177 |
Number of pages | 15 |
Journal | Journal Of Mathematical Biology |
Volume | 17 |
Issue number | 2 |
DOIs | |
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