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ISRN Biomathematics
Volume 2012 (2012), Article ID 471653, 23 pages
http://dx.doi.org/10.5402/2012/471653
Research Article

Dynamics of Single-City Influenza with Seasonal Forcing: From Regularity to Chaos

Centre for Nutrition Modelling, Department of Animal and Poultry Science, University of Guelph, Guelph, ON, Canada N1G 2W1

Received 7 September 2011; Accepted 17 October 2011

Academic Editors: C. B-Rao and I. Rogozin

Copyright © 2012 John H. M. Thornley and James France. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Seasonal and epidemic influenza continue to cause concern, reinforced by connections between human and avian influenza, and H1N1 swine influenza. Models summarize ideas about disease mechanisms, help understand contributions of different processes, and explore interventions. A compartment model of single-city influenza is developed. It is mechanism-based on lower-level studies, rather than focussing on predictions. It is deterministic, without non-disease-status stratification. Categories represented are susceptible, infected, sick, hospitalized, asymptomatic, dead from flu, recovered, and one in which recovered individuals lose immunity. Most categories are represented with sequential pools with first-order kinetics, giving gamma-function progressions with realistic dynamics. A virus compartment allows representation of environmental effects on virus lifetime, thence affecting reproductive ratio. The model's behaviour is explored. It is validated without significant tuning against data on a school outbreak. Seasonal forcing causes a variety of regular and chaotic behaviours, some being typical of seasonal and epidemic flu. It is suggested that models use sequential stages for appropriate disease categories because this is biologically realistic, and authentic dynamics is required if predictions are to be credible. Seasonality is important indicating that control measures might usefully take account of expected weather.