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Original Articles

Simulation of influenza propagation: Model development, parameter estimation, and mitigation strategies

, , &
Pages 27-48 | Received 02 Jul 2013, Accepted 31 Dec 2013, Published online: 07 Mar 2014

References

  • ABM++ (2009) https://www.epimodels.org/midas/abmplusplus.do
  • Aleman, D.M., Wibisono, T.G., and Schwartz, B. (2011) A nonhomogeneous agent-based simulation approach to modeling the spread of disease in a pandemic outbreak. Interfaces, 41(3), 301–315.
  • Andradóttir, S., Chiu, W., Goldsman, D., Lee, M.L., Tsui, K.-L., Sander, B., Fisman, D.N., and Nizam, A. (2011). Reactive strategies for containing developing outbreaks of pandemic influenza. BMC Public Health, 11(Suppl 1), S1. doi:10.1186/1471-2458-11-S1-S1.
  • Araz, O.M., Damien, P., Paltiel, D.A., Burke, S., Geijin, D., Galvani, A., and Meyers, L.A. (2012a) Simulating school closure policies for cost effective pandemic decision making. BMC Public Health, 12, 449.
  • Araz, O.M., Jehn, M., Lant, T., and Fowler, J.W. (2012b) A new method of exercising pandemic preparedness through an interactive simulation and visualization. Journal of Medical Systems, 36,1475–1483.
  • Araz, O.M., Lant, T., Fowler, J.W., and Jehn, M. (2011) A simulation model for policy decision analysis: A case of pandemic influenza on a university campus. Journal of Simulation, 5, 89–100.
  • Araz, O.M., Lant, T., Fowler, J.W., and Jehn, M. (2013) Simulation modeling for pandemic decision making: A case study with bi-criteria analysis on school closures. Decision Support Systems, 55, 564–575.
  • Arino, J., Brauer, F., van den Driessche, P., Watmough, J., and Wu, J. (2008) A model for influenza with vaccination and antiviral treatment. Journal of Theoretical Biology, 253, 118–130.
  • Atkinson, M.P., and Wein, L.M. (2008) Quantifying the routes of transmission for pandemic influenza. Bulletin of Mathematical Biology, 70, 820–867.
  • Balcan, D., Hu, H., Goncalves, B., Bajardi, P., Poletto, C., Ramasco, J.J., Paolotti, D., Perra, N., Tizzoni, M., Broeck, W.V., Colizza, V., and Vespignani, A. (2009) Seasonal transmission potential and activity peaks of the new influenza A(H1N1): A Monte Carlo likelihood analysis based on human mobility. BMC Medicine, 7, 45.
  • Ballas, D., Clarke, G.P., and Turton, I. (2003) A spatial microsimulation model for social policy microspatial analysis, in Boots, B., Okabe, A., and Thomas, R. (eds.), Modelling Geographical Systems: Statistical and Computational Applications, 143–168. Kluwer, Dordrecht.
  • Banks, J., Carson, J.S., Nelson, B.L., and Nicol, D.M. (2010) Discrete-Event System Simulation, 5th Ed., Prentice Hall, Englewood Cliffs, NJ.
  • Baroyan, O.V., Mironov, G.A., and Rvachev, L.A. (1981) An algorithm modeling global epidemics of mutant origin. Programming and Computer Software, 6(5), 272–277, . English translation from Programmirovanie, 5, 73–79 (1980) (in Russian).
  • Basta, N.E., Halloran, M.E., Matrajt, L., and Longini, I.M. Jr. (2008) Estimating influenza vaccine efficacy from challenge and community-based study data. American Journal of Epidemiology, 168, 1343–1352.
  • Beckman, R.J., Baggerly, K.A., and McKay, M.D. (1996) Creating synthetic baseline populations, Transportation Research, 30(6), 415–429.
  • Birkin, M., Turner, A., and Wu, B. (2006) A synthetic demographic model of the UK population: Methods, progress and problem. Proceedings of the 2nd International Conference on e-Social Science, Manchester, UK, . June, 2006.
  • Bisset, K.R., Chen, J., Feng, X., Kumar, V.S. A., and Marathe, M.V. (2009) EpiFast: A fast algorithm for large scale realistic epidemic simulations on distributed memory systems. Proceedings of the 23rd International Conference on Supercomputing, 430–439.
  • Boëlle, P.Y., Bernillon, P., and Desenclos, J.C. (2009) A preliminary estimation of the reproduction ratio for new influenza A (H1N1) from the outbreak in Mexico, March-April 2009. Eurosurveillance, 14(19), pii:19205.
  • Bowman, J.L., and Rousseau, G. (2008) Validation of Atlanta, Georgia, regional commission population synthesizer. Transportation Research Board Conference Proceedings, 2(42), 54–62.
  • Brauer, F. (2006) Some simple epidemic models. Emerging Infectious Diseases, 3(1), 1–15.
  • Brown, S.T., Tai, J.H. Y., Bailey, R.R., Cooley, P.C., Wheaton, W.D., Potter, M.A., Voorhees, R.E., LeJeune, M., Grefenstette, J.J., Burke, D.S., McGlone, S.M., and Lee, B.Y. (2011) Would school closure for the 2009 H1N1 influenza epidemic have been worth the cost?: A computational simulation of Pennsylvania. BMC Public Health, 11, 353. doi:10.1186/1471-2458-11-353.
  • Buckeridge, D.L., Burkom, H., Moore, A., Pavlin, J., Cutchis, P., and Hogan, W. (2004) Evaluation of syndromic surveillance systems–Design of an epidemic simulation model. Morbidity and Mortality Weekly Report, 53, September 24, 137–143.
  • Carrat, F., Luong, J., Lao, H., Sallé, A.-V., Lajaunie, C., and Wackernagel, H. (2006) A ‘small-world-like’ model for comparing interventions aimed at preventing and controlling influenza pandemics. BMC Medicine, 4(26), 1–14.
  • Carrat, F., Sahler, C., Leruez, M., Roger, S., Freymuth, F., Le Gales, C., Bungener, M., Housset, B., Nicolas, M., and Rouzioux, C. (2002) Influenza burden of illness: Estimates from a national prospective survey of household contacts in France. Archives of Internal Medicine, 162(16), 1842–1848.
  • Carrat, F., Vergu, E., Ferguson, N.M., Lemaitre, M., Cauchemez, S., Leach, S., and Valleron, A. (2008) Time lines of infection and disease in human influenza: A review of volunteer challenge studies. American Journal of Epidemiology, 167, 775–785.
  • Cauchemez, S., Carrat, F., Vibound, C., Valleron, A.J., and Boëlle, P.Y. (2004) A Bayesian MCMC approach to study transmission of influenza: Application to household longitudinal data. Statistics in Medicine, 23, 3469–3487.
  • Cauchemez, S., Donnelly, C.A., Reed, C., Ghani, A.C., Fraser, C., Kent, C.K., Finelli, L., and Ferguson, N.M. (2009) Household transmission of 2009 pandemic influenza A (H1N1) virus in the United States. The New England Journal of Medicine, 361(27), 2619–2627.
  • CDC (2010a) Social distancing law assessment template. . http://www.cdc.gov/phlp/publications/social_distancing.html
  • CDC (2010b) 2009 H1N1 flu (“Swine flu”) and you. . http://www. cdc.gov/h1n1flu/qa.htm
  • CDC (2010c) Interim recommendations for facemask and respirator use to reduce 2009 Influenza A (H1N1) virus transmission. . http://www.cdc.gov/h1n1flu/masks.htm
  • CDC (2012) Influenza antiviral drug resistance. . http://www.cdc.gov/flu/about/qa/antiviralresistance.htm
  • Chao, D.L., Halloran, M.E., Obenchain, V.J., and Longini, I.M. Jr. (2010) FluTE, a publicly available stochastic influenza epidemic simulation model. PLoS Computational Biology, 6(1), e1000656. . https://www.epimodels.org/midas/flute.do
  • Chong, N.S., Tchuenche, J.M., and Smith, R.J. (2013) A mathematical model of avian influenza with half-saturated incidence. Technical Report, Department of Mathematics, The University of Ottawa, Ottawa, Ontario, Canada.
  • Chowell, G., Ammon, C.E., Hengartnera, N.W., and Hymana, J.M. (2006) Estimation of the reproductive number of the Spanish flu epidemic in Geneva, Switzerland. Vaccine, 24, 6747–6750.
  • CNN (2009). . http://www.cnn.com/2009/HEALTH/04/28/flu.computer.modeling/index.html
  • Coburn, B.J., Wagner, B.G., and Blower, S. (2009) Modeling influenza epidemics and pandemics: Insights into the future of swine flu (H1N1). BMC Medicine, 22, 7–30.
  • Colizza, V., Barrat, A., Barthelemy, M., Valleron, A., and Vespignani, A. (2007) Modeling the worldwide spread of pandemic influenza: Baseline case and containment interventions. PLOS Medicine, 4(1), 95–109.
  • Cooper, B.S., Pitman, R.J., Edmunds, W.J., and Gay, N.J. (2006) Delay the international spread of pandemic influenza. PLOS Medicine, 3(6), 845–855.
  • Cowling, B.J., Ip, D.K. M., Fang, V.J., Suntarattiwong, P., Olsen, S.J., Levy, J., Uyeki, T.M., Leung, G.M., Peiris, J.S. M., Chotpitayasunondh, T., Nishiura, H., and Simmerman, J.M. (2013) Aerosol transmission is an important mode of influenza A virus spread. Nature Communications, 4, 1935, doi:10.1038/ncomms2922
  • Das, T.K., Savachkin, A.A., and Zhu, Y. (2008) A large-scale simulation model of pandemic influenza outbreaks for development of dynamic mitigation strategies. IIE Transactions, 40, 893–905.
  • Davey, V.J., Glass, R.J., Min, H.J., Beyeler, W.E., and Glass, L.M. (2008) Effective, robust design of community mitigation for pandemic influenza: A systematic examination of proposed US guidance. PLOS One, 3(7), e2606.
  • Del Valle, S.Y., Hyman, J.M., Hethcote, H.W., and Eubank, S.G. (2007) Mixing patterns between age groups in social networks. Social Networks, 29, 539–554.
  • Demicheli, V., Di Pietrantonj, C., Jefferson, T., Rivetti, A., and Rivetti, D. (2009) Vaccines for preventing influenza in healthy adults. . Cochrane review, prepared and maintained by The Cochrane Collaboration and published in The Cochrane Library 2009, Issue 2. John Wiley & Sons, Ltd. . (http://www.thecochranelibrary.com)
  • Dibble, C. (2010) Effective real-time allocation of pandemic interventions. In Johansson, B., Jain, S., Montoya-Torres, J., Hugan, J., and Yücesan, E. (eds.), Proceedings of the 2010 Winter Simulation Conference. Baltimore, Maryland, December, 2010, 2211–2220. . Institute of Electrical and Electronics Engineers, Piscataway, NJ.
  • Dorjee, S., Poljak, Z., Revie, C.W., Bridgland, J., McNab, B., Leger, E., and Sanchez, J. (2012) A review of simulation modelling approaches used for the spread of zoonotic influenza viruses in animal and human populations. Zoonoses and Public Health, doi:10.1111/zph.12010.
  • Ekici, A., Keskinocak, P., and Swann, J.L. (2008) Pandemic influenza response. In Mason, S.J., Hill, R.R., Moench, L., Rose, O. (eds.), Proceedings of the 2008 Winter Simulation Conference. Miami, Florida, December, 2008, 1592–1600. Institute of Electrical and Electronics Engineers, Piscataway, NJ.
  • Epstein, J.M., Goedecke, D.M., Yu, F., Morris, R.J., Wagener, D.K., and Bobashev, G.V. (2007) Controlling pandemic flu: The value of international air travel restrictions. PLOS One, 5, e401.
  • Eubank, S., Guclu, H., Kumar, V.S. A., Marathe, M.V., Srinivasan, A., Toroczkai, Z., and Wang, N. (2004) Modelling disease outbreaks in realistic urban social networks. Nature, 429, 180–184. . http://ndssl.vbi.vt.edu/episims.php
  • Ferguson, N.M., Anderson, R.M., and Garnett, G.P. (1996) Mass vaccination to control chickenpox: The influence of zoster. Proceedings of the National Academy of Sciences of the United States of America, 93, 7231–7235.
  • Ferguson, N.M., Cummings, D.A. T., Cauchemez, S., Fraser, C., Riley, S., Meeyai, A., Iamsirithaworn, S., and Burke, D.S. (2005) Strategies for containing an emerging influenza pandemic in Southeast Asia. Nature, 437, (8), 209–214.
  • Ferguson, N.M., Cummings, D.A. T., Fraser, C., Cajka, J.C., Cooley, P.C., and Burke, D.S. (2006) Strategies for mitigating an influenza pandemic. Nature, 442(27), 448–451.
  • Ferguson, N.M., Mallett, S., Jackson, H., Roberts, N., and Ward, P. (2003) A population-dynamic model for evaluating the potential spread of drug-resistant influenza virus infections during community-based use of antivirals. Journal of Antimicrobial Chemotherapy, 51, 977–990.
  • Fraser, C., Donnelly, C.A., Cauchemez, S., Hanage, W.P., Kerkhove, M.D. V., Hollingsworth, T.D., Griffin, J., Baggaley, R.F., Jenkins, H.E., Lyons, M.J., Jombart, T., Hinsley, W.R., Grassly, N.C., Balloux, F., Ghani, A.C., Ferguson, N.M., Rambaut, A., Pybus, O.G., Lopez-Gatell, H., Alpuche-Aranda, C.M., Chapela, B.I., Zavala, E.P., Guevara, D.M. E., Checchi, F., Garcia, E., Hugonnet, S., and Roth C for The WHO Rapid Pandemic Assessment Collaboration. (2009) Pandemic potential of a strain of influenza A (H1N1): Early findings. Science, 324(5934), 1227–1561.
  • Fumanelli, L., Ajelli, M., Manfredi, P., Vespignani, A., and Merler, S. (2012) Inferring the structure of social sontacts from demographic data in the analysis of infectious diseases spread. PLoS Computational Biology, 8(9), e1002673. doi:10.1371/journal.pcbi.1002673.
  • Germann, T.C., Kadau, K., Longini, I.M. Jr., and Macken, C.A. (2006) Mitigation strategies for pandemic influenza in the United States. Proceedings of the National Academy of Sciences of the United States of America, 103, 5935–5940.
  • Glass, R.J., Glass, L.M., Beyeler, W.E., and Min, H.J. (2006) Targeted social distancing design for pandemic influenza. Emerging Infectious Diseases, 12(11), 1671–1681.
  • Goedecke, D.M., Bobashev, G.V., and Yu, F. (2007a) A stochastic equation-based model of the value of international air-travel restrictions for controlling pandemic flu. In Henderson, S.G., Biller, B., Hsieh, M.H., Shortle, J., Tew, J.D., and Barton, R.R. (eds.), Proceedings of the 2007 Winter Simulation Conference, . Washington, DC, 1538–1542. Institute of Electrical and Electronics Engineers, Piscataway, NJ.
  • Goedecke, D.M., Yu, F., Bobashev, G., Epstein, J.M., and Morris, R.J. (2007b) User's manual of Global Epidemic Model (GEM): Stochastic equation-based model of a global epidemic. Research report, RTI international, Research Triangle Park, NC. . https://www.epimodels.org/midasdocs/GlobalModel/Global_Epidemic_Model_Manual.pdf
  • Gojovic, M.Z., Sander, B., Fisman, D., Krahn, M.D., and Bauch, C.T. (2009) Modelling mitigation strategies for pandemic (H1N1) 2009. Canadian Medical Association Journal, 181(10), 673–680.
  • Grais, R.F., Ellis, J.H., and Glass, G.E. (2003) Assessing the impact of airline travel on the geographic spread of pandemic influenza. European Journal of Epidemiology, 18, 1065–1072.
  • Grassly, N.C., and Fraser, C. (2008) Mathematical models of infectious disease transmission, Nature Review Microbiology, 6, 477–487.
  • Grenfell, B.T., and Anderson, R.M. (1985) The estimation of age-related rates of infection from case notifications and serological data. Journal of Hygiene, 95, 419–436.
  • Haber, M.J., Shay, D.K., Xiahoung, M.D., Patel, R., Xiaoping, J., Weintraub, E., Orenstein, E., and Thompson, W.W. (2007) Effectiveness of interventions to reduce contact rates during a simulated influenza pandemic. Emerging Infectious Diseases, 13(4), 581–589.
  • Halder, N., Kelso, J.K., and Milne, G.J. (2010) Developing guidelines for school closure interventions to be used during a future influenza pandemic. BMC Infectious Disease, 10, 221.
  • Halloran, M.E., Ferguson, N.M., Eubank, S., Longini, I.M. Jr., Cummings, D.A. T., Lewis, B., Xu, S., Fraser, C., Vullikanti, A., Germann, T.C., Wagener, D., Beckman, R., Kadau, K., Barrett, C., Macken, C.A., Burke, D.S., and Cooley, P. (2008) Modeling targeted layered containment of an influenza pandemic in the United States. Proceedings of the National Academy of Sciences of the United States of America, 105(12), 4639–4644. . http://www.pnas.org/cgi/doi/10.1073/pnas.0706849105
  • Halloran, M.E., Longini, I.M. Jr., Cowart, D.M., and Nizam, A. (2002a) Community interventions and the epidemic prevention potential. Vaccine, 20, 3254–3262.
  • Halloran, M.E., Longini, I.M. Jr., Nizam, A., and Yang, Y. (2002b) Containing bioterrorist smallpox. Science, 298, 1428–1432.
  • Halloran, M.E., Longini, I.M. Jr., and Struchiner, C.J. (1999) Design and interpretation of vaccine field studies. Epidemiological Review, 21(1), 73–88.
  • Hancock, K., Veguilla, V., Lu, X., Zhong, W., Butler, E.N., Sun, H., Liu, F., Dong, L., DeVos, J.R., Gargiullo, P.M., Brammer, T.L., Cox, N.J., Tumpey, T.M., and Katz, M. (2009) Crossreactive antibody responses to the 2009 pandemic H1N1 influenza virus. New England Journal of Medicine, 361, 1945–1952.
  • Handel, A., Longini, I.M., and Antia, R. (2009) Antiviral resistance and the control of pandemic influenza: The roles of stochasticity, evolution and model details. Journal of Theoretical Biology, 256(1), 117–125.
  • Hayden, F.G., Belshe, R., Villanueva, C., Lanno, R., Hughes, C., Small, I., Dutkowski, R., Ward, P., and Carr, J. (2004) Management of influenza in households: A prospective, randomized comparison of oseltamivir treatment with or without post-exposure prophylaxis. Journal of Infectious Diseases, 189, 440–449.
  • Heesterbeek, J.A. P. (2002) A brief history of R0 and a recipe for its calculation. Acta Biotheoretica, 50, 189–204.
  • Heffernan, J.M., Smith, R.J., and Wahl, L.M. (2005) Perspectives on the basic reproductive ratio. The Journal of the Royal Society Interface, 2(4), 281–293.
  • Jackson, C., Vynnycky, E., and Mangtani, P. (2010) Estimates of the transmissibility of the 1968 (Hong Kong) influenza pandemic: Evidence of increased transmissibility between successive waves. American Journal of Epidemiology, 171(4), 465–478.
  • Kelly, H., Carville, K., Grant, K., Jacoby, P., Tran, T., and Barr, I. (2009) Estimation of influenza vaccine effectiveness from routine surveillance data. PLoS ONE, 4(3), e5079.
  • Larson, R.C. (2007) Simple models of influenza progression within a heterogeneous population. Operations Research, 55(3), 399–412.
  • Law, A.M. (2007) Simulation Modeling and Analysis, 4th Ed., McGraw-Hill, New York.
  • Lee, B.Y., Brown, S.T., Cooley, P., Grefenstette, J.J., Zimmerman, R.K., Zimmer, S.M., Potter, M.A., Rosenfeld, R., Wheaton, W.D., Wiringa, A.E., Bacon, K.M., and Burke, D.S. (2010) Vaccination deep into a pandemic wave: Potential mechanisms for a “third wave” and the impact of vaccination. American Journal of Preventive Medicine, 39(5), 21–29.
  • Liu, C. (2004) Chinese Law on SARS (Chinese Law Series) 79–80. William S. Hein & Company, Buffalo, NY.
  • Lofgren, E., Fefferman, N.H., Naumov, Y.N., Gorski, J., and Naumova, E.N. (2007) Influenza seasonality: Underlying causes and modelling theories. Journal of Virology, 81(11), 5429–5436.
  • Longini, I.M. Jr., Halloran, M.E., Nizam, A., and Yang, Y. (2004) Containing pandemic influenza with antiviral agents. American Journal of Epidemiology, 159, 623–633.
  • Longini, I.M. Jr., Koopman, J.S., Haber, M., and Cotsonis, G.A. (1988) Statistical inference for infectious disease: Risk-specific household and community transmission parameters. American Journal of Epidemiology, 128(4), 845–859.
  • Longini, I.M. Jr., Koopman, J.S., Monto, A.S., and Fox, J.P. (1982) Estimating household and community transmission parameters for influenza. American Journal of Epidemiology, 115(5), 736–751.
  • Longini, I.M. Jr., Nizam, A., Xu, S., Ungchusak, K., Hanshaoworakul, W., Cummings, D.A. T., and Halloran, M.E. (2005) Containing pandemic influenza at the source. Science, 309, 1083–1087.
  • Los Alamos National Laboratory. (2008) TRANSIM 3.1 documentation set. Los Alamos National Laboratory, Los Alamos, NM. . http://ndssl.vbi.vt.edu/transims-docs.php
  • MacIntyre, C.R., Cauchemez, S., Dwyer, D.E., Seale, H., Cheung, P., Browne, G., Fasher, M., Wood, J., Gao, Z., Booy, R., and Ferguson, N. (2009) Face mask use and control of respiratory virus transmission in households. Emerging Infectious Diseases, 15 (2), 233–241.
  • Magalhaes, R.S., Pfeiffer, D., Wieland, B., Dung, D., and Otte, J. (2006) Commune-level simulation model of HPAI H5N1 poultry infection and control in Viet Nam. Pro-Poor Livestock Policy Initiative Research Report Nr. 06-07, Food and Agriculture Organization of the United Nations, Rome, Italy.
  • McKendrick, A.G. (1925) Applications of mathematics to medical problems. Proceedings of the Edinburgh Mathematical Society, 44, 98–130. Cambridge University Press, Edinburgh, UK. doi:10.1017/S0013091500034428.
  • Medlock, J., and Galvani, A.P. (2009) Optimizing influenza vaccine distribution. Science, 325, 1705–1708.
  • Meltzer, M.I., Cox, N.J., and Fukuda, K. (1999) The economic impact of pandemic influenza in the United States: Priorities for intervention. Emerging Infectious Diseases, 5(5), 659–671.
  • Mills, C.E., Robins, J.M., and Lipsitch, M. (2004) Transmissibility of 1918 pandemic influenza. Nature, 432(16), 904–906.
  • Milne, G.J., Kelso, J.K., Kelly, H.A., Huband, S.T., and McVernon, J. (2008) A small community model for the transmission of infectious diseases: Comparison of school closure as an intervention in individual-based models of an influenza pandemic. PLoS ONE, 3(12), e4005. doi:10.1371/journal.pone.0004005.
  • Moser, M.R., Bender, T.R., Margolis, H.S., Noble, G.R., Kendal, A.P., and Ritter, D.G. (1979) An outbreak of influenza aboard a commercial airliner. American Journal of Epidemiology, 110, 1–6.
  • Mossong, J., Hens, N., Jit, M., Beutels, P., Auranen, K., Mikolajczyk, R., Massari, M., Salmaso, S., Tomba, G.S., Wallinga, J., Heijne, J., Sadkowska-Todys, M., Rosinska, M., and Edmunds, W.J. (2008) Social contacts and mixing patterns relevant to the spread of infectious diseases. PLoS Medicine, 5(3), 381–391.
  • Nelson, B.L. (2013) Foundations and Methods of Stochastic Simulation: A First Course, Springer-Verlag, New York.
  • Özaltın, O., Prokopyev, O.A., Schaefer, A.J., and Roberts, M.S. (2011) Optimizing the societal benefits of the annual influenza vaccine: A stochastic programming approach. Operations Research, 59(5), 1131–1143.
  • Patel, R., Longini, I.M. Jr., and Halloran, M.E. (2005) Finding optimal vaccination strategies for pandemic influenza using genetic algorithms. Journal of Theoretical Biology, 234, 201–212.
  • Public Use Microdata Samples (PUMS). (1990) Census of population and housing, US Census Bureau, . http://www.census.gov/main/www/pums.html
  • Rees, P., Martin, D., and Williamson, P. (2002) The Census Data System. John Wiley & Sons, London, UK.
  • Ridenhour, B.J., Braun, A., Teyrasse, T., and Goldsman, D. (2011) Controlling the spread of disease in schools. PLoS ONE, 6(12), e29640.
  • Rvachev, L.A., and Longini, I.M. (1985) A mathematical model for the global spread of influenza. Mathematical Biosciences, 75, 3–22.
  • Sandora, T.J. (2008) Reducing absenteeism from gastrointestinal and respiratory illness in elementary school students: A randomized, controlled trial of an infection-control intervention. Pediatrics, 121(6), e1555. doi:10.1542/peds.2007-2597.
  • Schenzle, D. (1984) An age-structured model of pre- and post-vaccination measles transmission. IMA Journal of Mathematics Applied in Medicine and Biology, 1, 169–191.
  • Singer, A.C., Howard, B.M., Johnson, A.C., Knowles, C.J., Jackman, S.J., Accinelli, C., Caracciolo, A.B., Bernard, I., Bird, S., Boucard, T., Boxall, A., Brian, J.V., Cartmell, E., Chubb, C., Churchley, J., Costigan, S., Crane, M., Cempsey, M.J., Dorrington, B., Ellor, B., Fick, J., Holmes, J., Hutchinson, T., Carcher, F., Kelleher, S.L., Marsden, P., Noone, G., Nunn, M.A., Oxford, J., Rachwal, T., Roberts, N., Roberts, M., Saccà, M.L., Sanders, M., Straub, J.O., Terry, A., Thomas, D., Toovey, S., Townsend, R., Voulvoulis, N., and Watts, C. (2008) Meeting reports: Risk assessment of Tamiflu use under pandemic conditions. Environmental Health Perspectives, 116(11), 1563–1567.
  • Smith, R. (2008) Modelling Disease Ecology with Mathematics. American Institute of Mathematical Sciences Springfield, Missouri.
  • St. John, R.K., King, A., de Jong, D., Bodie-Collins, M., Squires, S.G., and Tam, T.W. (2005) Border screening for SARS. Emerging Infectious Diseases, 11(1), 6–10.
  • Stuart-Harris, C.H. (1970) Pandemic influenza: An unresolved problem in prevention. Journal of Infectious Diseases, 122, 108–115.
  • Tuite, A.R., Greer, A., Kwong, J.C., and Fisman, D.N. (2010a) Optimal pandemic influenza vaccine allocation strategies for the Canadian population. PLoS ONE, 5(5), e10520. . http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2865540/pdf/pone.0010520.pdf
  • Tuite, A.R., Greer, A.L., Whelan, M., Winter, A.-L., Lee, B., Yan, P., Wu, J., Moghadas, S., Buckeridge, D., Pourbohloul, B., and Fisman, D.N. (2010b) Estimated epidemiologic parameters and morbidity associated with pandemic H1N1 influenza. Canadian Medical Association Journal, 182(2), 131–136.
  • U.S. News & World Report. (2009) Swine flu vaccination should target children first. . http://www.usnews.com/science/articles/2009/09/10/swine-flu-vaccination-should-target-children-first.html.
  • Viboud, C., Bjornstad, O.N., Smith, D.L., Simonsen, L., Miller, M.A., and Grenfell, B.T. (2006) Synchrony, waves and spatial hierarchies in the spread of influenza. Science, 312, 447–451.
  • Weinberg, G.A., and Szilagyi, P.G. (2010) Vaccine epidemiology: Efficacy, effectiveness, and the translational research roadmap. Journal of Infectious Diseases, 201(11), 1607–1610.
  • Welliver, R., Monto, A.S., Carewicz, O., Schatteman, E., Hassman, M., Hedrick, J., Jackson, H.C., Huson, L., Ward, P., and Oxford, J.S., for the Oseltamivir Post Exposure Prophylaxis Investigator Group. (2001) Effectiveness of oseltamivir in preventing influenza in household contacts: A randomized controlled trial. Journal of the American Medical Association, 285, 748–754.
  • Weycker, D., Edelsberg, J., Halloran, M.E., Longini, I.M. Jr., Nizam, A., Ciuryla, V., and Oster, G. (2005) Population-wide benefits of routine vaccination of children against influenza. Vaccine, 23, 1284–1293.
  • Wheaton, W.D., Cajka, J.C., Chasteen, B.M., Wagener, D.K., Cooley, P.C., Ganapathi, L., Roberts, D.J., and Allpress, J.L. (2009) Synthesized population databases: A US geospatial database for agent-based models, Methods report, RTI Press, Research Triangle Park, NC. . http://www.rti.org/pubs/mr-0010-0905-wheaton.pdf
  • Wikipedia. (2012a) Compartmental models in epidemiology. . http://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology#The_SIS_model
  • Wikipedia. (2012b) Influenza. . http://en.wikipedia.org/wiki/Influenza
  • Williamson, P., Birkin, M., and Rees, P. (1998) The estimation of population microdata by using data from small area statistics and samples of anonymised records. Environment and Planning A, 30, 785–816.
  • Wu, J.T., Wein, L.M., and Perelson, A.S. (2005) Optimization of influenza vaccine selection. Operations Research, 53(3), 456–476.
  • Wu, J.T., Riley, S., Fraser, C., and Leung, G.L. (2006) Reducing the impact of the next influenza pandemic using household-based public health interventions. PLoS Medicine, 3(9), 1532–1540.
  • Wu, J.T., Riley, S., Fraser, C., and Leung, G.M. (2007) Spatial considerations for the allocation of pre-pandemic influenza vaccination in the United States. Proceeding of The Royal Society B, 274, 2811–2817. . The Royal Society, London, UK.
  • Wu, J.T., Lee, C.K., Cowling, B.J., and Yuen, K.Y. (2010) Logistical feasibility and potential benefits of a population–wide passive-immunotherapy program during an influenza pandemic. Proceedings of the National Academy of Sciences of the United States of America, 107(7), 3269–3274.
  • Yang, Y., Halloran, M.E., Sugimoto, J., and Longini, I.M. (2007) Detecting human-to-human transmission of avian influenza A (H5N1). Emerging Infectious Diseases, 13(9), 1348–1353.
  • Yang, Y., Longini, I.M. Jr., and Halloran, M.E. (2006) Design and evaluation of prophylactic interventions using infectious disease incidence data from close contact groups. Journal of the Royal Statistical Society: Series C Applied Statistics, 55, 317–330.
  • Yang, Y., Sugimoto, J.D., Halloran, M.E., Basta, N.E., Chao, D.L., Matrajt, L., Potter, G., Kenah, E., and Longini, I.M. Jr. (2009) The transmissibility and control of pandemic influenza A (H1N1) virus. Science, 326, 729–733.
  • Zagheni, E., Billari, F.C., Manfredi, P., Melegaro, A., Mossong, J., and Edmunds, W.J. (2008) Using time-use data to parameterize models for the spread of close-contact infectious disease. American Journal of Epidemiology, 168(9), 1082–1090.

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