Long Period Trajectories of the Seasonal SIR Model

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Creator: 

Finney, Lucas Angelo

Date: 

2021

Abstract: 

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)

Subject: 

Mathematics
Epidemiology

Language: 

English

Publisher: 

Carleton University

Thesis Degree Name: 

Master of Science: 
M.Sc.

Thesis Degree Level: 

Master's

Thesis Degree Discipline: 

Mathematics

Parent Collection: 

Theses and Dissertations

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