Long Period Trajectories of the Seasonal SIR Model
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Many infectious diseases exhibit seasonally varying incidence rates. In order to mathematically describe and predict the behavior of such diseases, the seasonal susceptible-infected-removed (Seasonal SIR) model, a system of ordinary differential equations, was formulated. It has been found in numerical simulations of the Seasonal SIR model that sub-harmonic bifurcations may occur, leading to the appearance of periodic modes with inter-outbreak periods on the scale of two time units or more in response to a varying forcing of period one. In the extremes of these long inter-outbreak period modes, it has been observed that periodic modes on the order of nine time units or more may be found. Additionally, these long inter-outbreak period modes exhibit a behaviour of increasing outbreak severity as the time between outbreaks is lengthened. (Continued Within)
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Copyright © 2021 the author(s). Theses may be used for non-commercial research, educational, or related academic purposes only. Such uses include personal study, research, scholarship, and teaching. Theses may only be shared by linking to Carleton University Institutional Repository and no part may be used without proper attribution to the author. No part may be used for commercial purposes directly or indirectly via a for-profit platform; no adaptation or derivative works are permitted without consent from the copyright owner.
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- 2021
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finney-longperiodtrajectoriesoftheseasonalsirmodel.pdf | 2023-05-05 | Public | Download |