- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- Aims and Scope ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Volume 2012 (2012), Article ID 471653, 23 pages
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.
- E. Hak, M. J. Meijboom, and E. Buskens, “Modelling the health-economic impact of the next influenza pandemic in The Netherlands,” Vaccine, vol. 24, no. 44–46, pp. 6756–6760, 2006.
- N. A. M. Molinari, I. R. Ortega-Sanchez, M. L. Messonnier et al., “The annual impact of seasonal influenza in the US: measuring disease burden and costs,” Vaccine, vol. 25, no. 27, pp. 5086–5096, 2007.
- J. S. Nguyen-van-Tam and C. Sellwood, “Avian influenza and the threat of the next human pandemic,” Journal of Hospital Infection, vol. 65, no. 2, pp. 10–13, 2007.
- I. Capua and S. Marangon, “Control of avian influenza in poultry,” Emerging Infectious Diseases, vol. 12, no. 9, pp. 1319–1324, 2006.
- R. M. Anderson and R. M. May, Infectious Diseases of Humans: Dynamics and Control, Oxford University Press, Oxford, UK, 1991.
- O. Diekmann and J. Hesterbeek, Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation, Wiley, New York, NY, USA, 2000.
- M. Nuño, G. Chowell, and A. B. Gumel, “Assessing the role of basic control measures, antivirals and vaccine in curtailing pandemic influenza: scenarios for the US, UK and the Netherlands,” Journal of the Royal Society Interface, vol. 4, no. 14, pp. 505–521, 2007.
- M. Gauthier-Clerc, C. Lebarbenchon, and F. Thomas, “Recent expansion of highly pathogenic avian influenza H5N1: a critical review,” Ibis, vol. 149, no. 2, pp. 202–214, 2007.
- K. Van Reeth, “Avian and swine influenza viruses: our current understanding of the zoonotic risk,” Veterinary Research, vol. 38, no. 2, pp. 243–260, 2007.
- D. J. D. Earn, J. Dushoff, and S. A. Levin, “Ecology and evolution of the flu,” Trends in Ecology and Evolution, vol. 17, no. 7, pp. 334–340, 2002.
- C. M. Pease, “An evolutionary epidemiological mechanism, with applications to type a influenza,” Theoretical Population Biology, vol. 31, no. 3, pp. 422–452, 1987.
- O. A. Christophersen and A. Haug, “Why is the world so poorly prepared for a pandemic of hypervirulent avian influenza?” Microbial Ecology in Health and Disease, vol. 18, no. 3-4, pp. 113–132, 2006.
- T. Day, J. B. André, and A. Park, “The evolutionary emergence of pandemic influenza,” Proceedings of the Royal Society B: Biological Sciences, vol. 273, no. 1604, pp. 2945–2953, 2006.
- S. Iwami, Y. Takeuchi, and X. Liu, “Avian-human influenza epidemic model,” Mathematical Biosciences, vol. 207, no. 1, pp. 1–25, 2007.
- M. Nuño, Z. Feng, M. Martcheva, and C. Castillo-Chavez, “Dynamics of two-strain influenza with isolation and partial cross-immunity,” SIAM Journal on Applied Mathematics, vol. 65, no. 3, pp. 964–982, 2005.
- B. Hancioglu, D. Swigon, and G. Clermont, “A dynamical model of human immune response to influenza A virus infection,” Journal of Theoretical Biology, vol. 246, no. 1, pp. 70–86, 2007.
- G. A. Bocharov and A. A. Romanyukha, “Mathematical model of antiviral immune response III. Influenza a virus infection,” Journal of Theoretical Biology, vol. 167, no. 4, pp. 323–360, 1994.
- R. D. Balicer, M. Huerta, N. Davidovitch, and I. Grotto, “Cost-benefit of stockpiling drugs for influenza pandemic,” Emerging Infectious Diseases, vol. 11, no. 8, pp. 1280–1282, 2005.
- N. M. Ferguson, D. A. T. Cummings, S. Cauchemez et al., “Strategies for containing an emerging influenza pandemic in Southeast Asia,” Nature, vol. 437, no. 7056, pp. 209–214, 2005.
- R. Gani, H. Hughes, D. Fleming, T. Griffin, J. Medlock, and S. Leach, “Potential impact of antiviral drug use during influenza pandemic,” Emerging Infectious Diseases, vol. 11, no. 9, pp. 1355–1362, 2005.
- I. M. Longini Jr., A. Nizam, S. Xu et al., “Containing pandemic influenza at the source,” Science, vol. 309, no. 5737, pp. 1083–1087, 2005.
- B. Pourbohloul, L. A. Meyers, D. M. Skowronski, M. Krajden, D. M. Patrick, and R. C. Brunham, “Modeling control strategies of respiratory pathogens,” Emerging Infectious Diseases, vol. 11, no. 8, pp. 1249–1256, 2005.
- F. Carrat, J. Luong, H. Lao, A. V. Sallé, C. Lajaunie, and H. Wackernagel, “A “small-world-like” model for comparing interventions aimed at preventing and controlling influenza pandemics,” BMC Medicine, vol. 4, article 26, 2006.
- Y. H. Hsieh, C. C. King, C. W. S. Chen, M. S. Ho, S. B. Hsu, and Y. C. Wu, “Impact of quarantine on the 2003 SARS outbreak: a retrospective modeling study,” Journal of Theoretical Biology, vol. 244, no. 4, pp. 729–736, 2007.
- G. Chowell, C. E. Ammon, N. W. Hengartner, and J. M. Hyman, “Transmission dynamics of the great influenza pandemic of 1918 in Geneva, Switzerland: assessing the effects of hypothetical interventions,” Journal of Theoretical Biology, vol. 241, no. 2, pp. 193–204, 2006.
- M. Eichner, M. Schwehm, H. P. Duerr, and S. O. Brockmann, “The influenza pandemic preparedness planning tool InfluSim,” BMC Infectious Diseases, vol. 7, article 17, 2007.
- H. P. Duerr, S. O. Brockmann, I. Piechotowski, M. Schwehm, and M. Eichner, “Influenza pandemic intervention planning using InfluSim: pharmaceutical and non-pharmaceutical interventions,” BMC Infectious Diseases, vol. 7, article 76, 2007.
- A. L. Lloyd, “Destabilization of epidemic models with the inclusion of realistic distributions of infectious periods,” Proceedings of the Royal Society B: Biological Sciences, vol. 268, no. 1470, pp. 985–993, 2001.
- J. C. Hopkins and R. J. Leipold, “On the dangers of adjusting the parameter values of mechanism-based mathematical models,” Journal of Theoretical Biology, vol. 183, no. 4, pp. 417–427, 1996.
- S. A. Levin and R. Durrett, “From individuals to epidemics,” Philosophical Transactions of the Royal Society B: Biological Sciences, vol. 351, no. 1347, pp. 1615–1621, 1996.
- P. Sebastiani, K. D. Mandl, P. Szolovits, I. S. Kohane, and M. F. Ramoni, “A Bayesian dynamic model for influenza surveillance,” Statistics in Medicine, vol. 25, no. 11, pp. 1803–1816, 2006.
- J. Arino, F. Brauer, P. van den Driessche, J. Watmough, and J. Wu, “Simple models for containment of a pandemic,” Journal of the Royal Society Interface, vol. 3, no. 8, pp. 453–457, 2006.
- J. Shaman and M. Kohn, “Absolute humidity modulates influenza survival, transmission, and seasonality,” Proceedings of the National Academy of Sciences of the United States of America, vol. 106, no. 9, pp. 3243–3248, 2009.
- J. Dushoff, J. B. Plotkin, C. Viboud, D. J. D. Earn, and L. Simonsen, “Mortality due to influenza in the United States—an annualized regression approach using multiple-cause mortality data,” American Journal of Epidemiology, vol. 163, no. 2, pp. 181–187, 2006.
- T. A. Reichert, L. Simonsen, A. Sharma, S. A. Pardo, D. S. Fedson, and M. A. Miller, “Influenza and the winter increase in mortality in the United States, 1959–1999,” American Journal of Epidemiology, vol. 160, no. 5, pp. 492–502, 2004.
- G. A. Poland, “If you could halve the mortality rate, would you do it?” Clinical Infectious Diseases, vol. 35, no. 4, pp. 378–380, 2002.
- K. L. Nichol, J. Nordin, J. Mullooly, R. Lask, K. Fillbrandt, and M. Iwane, “Influenza vaccination and reduction in hospitalizations for cardiac disease and stroke among the elderly,” New England Journal of Medicine, vol. 348, no. 14, pp. 1322–1332, 2003.
- D. L. Crombie, D. M. Fleming, K. W. Cross, and R. J. Lancashire, “Concurrence of monthly variations of mortality related to underlying cause in Europe,” Journal of Epidemiology and Community Health, vol. 49, no. 4, pp. 373–378, 1995.
- B. M. Bolker and B. T. Grenfell, “Chaos and biological complexity in measles dynamics,” Proceedings of the Royal Society B: Biological Sciences, vol. 251, no. 1330, pp. 75–81, 1993.
- R. Casagrandi, L. Bolzoni, S. A. Levin, and V. Andreasen, “The SIRC model and influenza A,” Mathematical Biosciences, vol. 200, no. 2, pp. 152–169, 2006.
- J. Dushoff, J. B. Plotkin, S. A. Levin, and D. J. D. Earn, “Dynamical resonance can account for seasonality of influenza epidemics,” Proceedings of the National Academy of Sciences of the United States of America, vol. 101, no. 48, pp. 16915–16916, 2004.
- L. A. Rvachev and I. M. Longini, “A mathematical model for the global spread of influenza,” Mathematical Biosciences, vol. 75, no. 1, pp. 3–22, 1985.
- H. J. Wearing, P. Rohani, and M. J. Keeling, “Appropriate models for the management of infectious diseases,” PLoS Medicine, vol. 2, no. 7, Article ID e174, pp. 621–627, 2005.
- J. H. M. Thornley and J. France, Mathematical Models in Agriculture, CAB International, Wallingford, UK, 2007.
- C. E. Mills, J. M. Robins, and M. Lipsitch, “Transmissibility of 1918 pandemic influenza,” Nature, vol. 432, no. 7019, pp. 904–906, 2004.
- P. Wright and R. G. Webster, “Orthomyxoviruses,” in Fields Virology, D. M. Knipe, P. M. Howley, and D. E. Griffin, Eds., pp. 1533–1579, Lippincott, Williams and Wilkins, Philadelphia, Pa, USA, 2001.
- P. Baccam, C. Beauchemin, C. A. Macken, F. G. Hayden, and A. S. Perelson, “Kinetics of influenza A virus infection in humans,” Journal of Virology, vol. 80, no. 15, pp. 7590–7599, 2006.
- A. C. Lowen, S. Mubareka, J. Steel, and P. Palese, “Influenza virus transmission is dependent on relative humidity and temperature,” PLoS Pathogens, vol. 3, no. 10, Article ID e151, pp. 1470–1476, 2007.
- J. H. M. Thornley, Grassland Dynamics: An Ecosystem Simulation Model, CAB International, Wallingford, UK, 1998.
- M. P. Taylor, “Influenza 1969-1970. Incidence in general practice based on a population survey,” Journal of the Royal College of General Practitioners, vol. 21, no. 102, pp. 17–22, 1971.
- J. Fry, “Epidemic influenza. Patterns over 20 years (1949–1968),” Journal of the Royal College of General Practitioners, vol. 17, no. 79, pp. 100–103, 1969.
- B. J. Coburn, B. G. Wagner, and S. Blower, “Modeling influenza epidemics and pandemics: insights into the future of swine flu (H1N1),” BMC Medicine, vol. 7, article 30, 2009.
- Anon, “Influenza in a boarding school,” British Medical Journal, vol. 1, p. 587, 1978.
- K. Popper, The Poverty of Historicism, Routledge & Kegan Paul, London, UK, 1957.
- A. Flahault, S. Deguen, and A. J. Valleron, “A mathematical model for the European spread of influenza,” European Journal of Epidemiology, vol. 10, no. 4, pp. 471–474, 1994.
- A. Flahault, S. Letrait, P. Blin, S. Hazout, J. Menares, and A. J. Valleron, “Modelling the 1985 influenza epidemic in France,” Statistics in Medicine, vol. 7, no. 11, pp. 1147–1155, 1988.
- N. P. Johnson and J. Mueller, “Updating the accounts: global mortality of the 1918–1920 “Spanish” influenza pandemic,” Bulletin of the History of Medicine, vol. 76, no. 1, pp. 105–115, 2002.