As recently pointed out by the Institute of Medicine, the existing pandemic mitigation models lack the dynamic decision support capability. We develop a large-scale simulation-driven optimization model for generating dynamic predictive distribution of vaccines and antivirals over a network of regional pandemic outbreaks. The model incorporates measures of morbidity, mortality, and social distancing, translated into the cost of lost productivity and medical expenses. The performance of the strategy is compared to that of the reactive myopic policy, using a sample outbreak in Fla, USA, with an affected population of over four millions. The comparison is implemented at different levels of vaccine and antiviral availability and administration capacity. Sensitivity analysis is performed to assess the impact of variability of some critical factors on policy performance. The model is intended to support public health policy making for effective distribution of limited mitigation resources. 1. Introduction As of July 2010, WHO has reported 501 confirmed human cases of avian influenza A/(H5N1) which resulted in 287 deaths worldwide [1]. At the same time, the statistics for the H1N1 2009 outbreak has so far included 214 countries with a total reported number of infections and deaths of 419,289 and 18,239, respectively [2]. Today, an ominous expectation exists that the next pandemic will be triggered by a highly pathogenic virus, to which there is little or no pre-existing immunity in humans [3]. The nation's ability to mitigate a pandemic influenza depends on the available emergency response resources and infrastructure, and, at present, challenges abound. Predicting the exact virus subtype remains a difficult task, and even when identified, reaching an adequate vaccine supply can currently take up to nine months [4, 5]. Even if the existing vaccines prove to be potent, their availability will be limited by high production and inventory costs [6, 7] and also will be constrained by the supply of antiviral drugs, healthcare providers, hospital beds, medical supplies, and logistics. Hence, pandemic mitigation will have to be done amidst limited availability of resources and supporting infrastructure. This challenge has been acknowledged by WHO [7] and echoed by the HHS and CDC [8, 9]. The existing models on pandemic influenza (PI) containment and mitigation aims to address various complex aspects of the pandemic evolution process including: (i) the mechanism of disease progression, from the initial contact and infection transmission to the asymptomatic phase,
References
[1]
World Health Organization (WHO), “Cumulative number of confirmed human cases of Avian Influenza A(H5N1) reported to WHO,” 2010, http://www.who.int/csr/disease/avian_Influenza/country/cases_table_2010_07_05/en/index.html.
[2]
World Health Organization, “Pandemic (H1N1),” 2009, http://www.who.int/csr/don/2010_07_02/en/index.html.
[3]
A. Schoenstadt, “Spanish Flu,” 2009, http://flu.emedtv.com/spanish-flu/spanish-flu.html.
[4]
D. S. Fedson, “Pandemic Influenza and the global vaccine supply,” Clinical Infectious Diseases, vol. 36, no. 12, pp. 1552–1561, 2003.
[5]
J. Aunins, A. Lee, and D. Volkin, Vaccine Production, CRC Press, Boca Raton, Fla, USA, 2nd edition, 2000.
[6]
World Health Organization, “Pandemic (h1n1) vaccine deployment,” 2009, http://www.who.int/csr/disease/swineflu/vaccines/h1n1_vaccination_deployment_update_20091217.pdf.
[7]
WHO Global Influenza Programme, “Pandemic Influenza preparedness and response,” Tech. Rep., World Health Organization, Lyon, France, 2009.
[8]
Centers for Disease Control and Prevention (CDC), “Preparing for pandemic Influenza,” 2007, http://www.cdc.gov/flu/pandemic/preparedness.htm.
[9]
U.S. Department of Health & Human Services, “HHS pandemic influenza plan,” 2007, http://www.hhs.gov/pandemicflu/plan/.
[10]
A. Handel, I. Longini, and R. Antia, “Towards a quantitative understanding of the within-host dynamics of Influenza A infections,” Epidemics, vol. 1, no. 3, pp. 185–195, 2009.
[11]
B. Pourbohloul, A. Ahued, B. Davoudi et al., “Initial human transmission dynamics of the pandemic (H1N1) 2009 virus in North America,” Influenza and other Respiratory Viruses, vol. 3, no. 5, pp. 215–222, 2009.
[12]
M. P. Atkinson and L. M. Wein, “Quantifying the routes of transmission for pandemic Influenza,” Bulletin of Mathematical Biology, vol. 70, no. 3, pp. 820–867, 2008.
[13]
V. E. Pitzer, S. J. Olsen, C. T. Bergstrom, S. F. Dowell, and M. Lipsitch, “Little evidence for genetic susceptibility to Influenza A (H5N1) from family clustering data,” Emerging Infectious Diseases, vol. 13, no. 7, pp. 1074–1076, 2007.
[14]
V. E. Pitzer, G. M. Leung, and M. Lipsitch, “Estimating variability in the transmission of severe acute respiratory syndrome to household contacts in Hong Kong, China,” American Journal of Epidemiology, vol. 166, no. 3, pp. 355–363, 2007.
[15]
Y. Yang, J. D. Sugimoto, M. Elizabeth Halloran et al., “The transmissibility and control of pandemic Influenza a (H1N1) virus,” Science, vol. 326, no. 5953, pp. 729–733, 2009.
[16]
Y. Yang, M. E. Halloran, J. D. Sugimoto, and I. M. Longini, “Detecting human-to-human transmission of avian Influenza A (H5N1),” Emerging Infectious Diseases, vol. 13, no. 9, pp. 1348–1353, 2007.
[17]
S. Cauchemez, F. Carrat, C. Viboud, A. J. Valleron, and P. Y. Bo？lle, “A Bayesian MCMC approach to study transmission of Influenza: application to household longitudinal data,” Statistics in Medicine, vol. 23, no. 22, pp. 3469–3487, 2004.
[18]
V. Colizza, A. Barrat, M. Barthélemy, and A. Vespignani, “The role of the airline transportation network in the prediction and predictability of global epidemics,” Proceedings of the National Academy of Sciences of the United States of America, vol. 103, no. 7, pp. 2015–2020, 2006.
[19]
J. M. Epstein, J. Parker, D. Cummings, and R. A. Hammond, “Coupled contagion dynamics of fear and disease: mathematical and computational explorations,” PLoS ONE, vol. 3, no. 12, Article ID e3955, 2008.
[20]
M. E. Halloran, “Invited commentary: challenges of using contact data to understand acute respiratory disease transmission,” American Journal of Epidemiology, vol. 164, no. 10, pp. 945–946, 2006.
[21]
F. G. Ball and O. D. Lyne, “Optimal vaccination policies for stochastic epidemics among a population of households,” Mathematical Biosciences, vol. 177-178, pp. 333–354, 2002.
[22]
N. G. Becker and D. N. Starczak, “Optimal vaccination strategies for a community of households,” Mathematical Biosciences, vol. 139, no. 2, pp. 117–132, 1997.
[23]
F. Carrat, A. Lavenu, S. Cauchemez, and S. Deleguer, “Repeated Influenza vaccination of healthy children and adults:borrow now, pay later?” Epidemiology and Infection, vol. 134, no. 1, pp. 63–70, 2005.
[24]
N. M. Ferguson, S. Mallett, H. Jackson, N. Roberts, and P. Ward, “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, vol. 51, no. 4, pp. 977–990, 2003.
[25]
P. Y. Lee, D. B. Matchar, D. A. Clements, J. Huber, J. D. Hamilton, and E. D. Peterson, “Economic analysis of Influenza vaccination and antiviral treatment for healthy working adults,” Annals of Internal Medicine, vol. 137, no. 4, pp. 225–231, 2002.
[26]
M. Lipsitch, T. Cohen, M. Murray, and B. R. Levin, “Antiviral resistance and the control of pandemic Influenza,” PLoS Medicine, vol. 4, no. 1, pp. 111–121, 2007.
[27]
G. J. Milne, J. K. Kelso, H. A. Kelly, S. T. Huband, and J. McVernon, “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, vol. 3, no. 12, Article ID e4005, 2008.
[28]
H. Yasuda and K. Suzuki, “Measures against transmission of pandemic H1N1 Influenza in Japan in 2009: simulation model,” Euro Surveillance : Bulletin Européen sur les Maladies Transmissibles = European Communicable Disease Bulletin, vol. 14, no. 44, 2009.
[29]
G. Miller, S. Randolph, and J. E. Patterson, “Responding to simulated pandemic Influenza in San Antonio, Texas,” Infection Control and Hospital Epidemiology, vol. 29, no. 4, pp. 320–326, 2008.
[30]
J. K. Kelso, G. J. Milne, and H. Kelly, “Simulation suggests that rapid activation of social distancing can arrest epidemic development due to a novel strain of Influenza,” BMC Public Health, vol. 9, article 117, 2009.
[31]
N. Halder, J. Kelso, and G. Milne, “Analysis of the effectiveness of interventions used during the 2009 A/H1N1 Influenza pandemic,” BioMed Central, vol. 10, article 168, 2010.
[32]
D. O. Scharfstein, M. E. Halloran, H. Chu, and M. J. Daniels, “On estimation of vaccine efficacy using validation samples with selection bias,” Biostatistics, vol. 7, no. 4, pp. 615–629, 2006.
[33]
R. J. Glass, L. M. Glass, W. E. Beyeler, and H. J. Min, “Targeted social distancing design for pandemic Influenza,” Emerging Infectious Diseases, vol. 12, no. 11, pp. 1671–1681, 2006.
[34]
K. R. Nigmatulina and R. C. Larson, “Living with Influenza: impacts of government imposed and voluntarily selected interventions,” European Journal of Operational Research, vol. 195, no. 2, pp. 613–627, 2009.
[35]
I. M. Longini, M. E. Halloran, A. Nizam, and Y. Yang, “Containing pandemic Influenza with antiviral agents,” American Journal of Epidemiology, vol. 159, no. 7, pp. 623–633, 2004.
[36]
J. T. Wu, S. Riley, C. Fraser, and G. M. Leung, “Reducing the impact of the next Influenza pandemic using household-based public health interventions,” PLoS Medicine, vol. 3, no. 9, pp. 1532–1540, 2006.
[37]
C. E. Mills, J. M. Robins, and M. Lipsitch, “Transmissibility of 1918 pandemic Influenza,” Nature, vol. 432, no. 7019, pp. 904–906, 2004.
[38]
R. Patel, I. M. Longini, and M. E. Halloran, “Finding optimal vaccination strategies for pandemic Influenza using genetic algorithms,” Journal of Theoretical Biology, vol. 234, no. 2, pp. 201–212, 2005.
[39]
V. Colizza, A. Barrat, M. Barthelemy, A. J. Valleron, and A. Vespignani, “Modeling the worldwide spread of pandemic Influenza: baseline case and containment interventions,” PLoS Medicine, vol. 4, no. 1, pp. 95–110, 2007.
[40]
P. Cooley, L. Ganapathi, G. Ghneim, S. Holmberg, W. Wheaton, and C. R. Hollingsworth, “Using Influenza-like illness data to reconstruct an Influenza outbreak,” Mathematical and Computer Modelling, vol. 48, no. 5-6, pp. 929–939, 2008.
[41]
D. L. Chao, M. E. Halloran, V. J. Obenchain, and I. M. Longini, “FluTE, a publicly available stochastic Influenza epidemic simulation model,” PLoS Computational Biology, vol. 6, no. 1, Article ID e1000656, 2010.
[42]
National Institute of General Medical Sciences, “Models of Infectious Disease Agent Study,” 2008, http://www.nigms.nih.gov/Initiatives/MIDAS/.
[43]
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.
[44]
I. M. Longini, A. Nizam, S. Xu et al., “Containing pandemic Influenza at the source,” Science, vol. 309, no. 5737, pp. 1083–1087, 2005.
[45]
N. M. Ferguson, D. A. T. Cummings, C. Fraser, J. C. Cajka, P. C. Cooley, and D. S. Burke, “Strategies for mitigating an Influenza pandemic,” Nature, vol. 442, no. 7101, pp. 448–452, 2006.
[46]
T. C. Germann, K. Kadau, I. M. Longini, and C. A. Macken, “Mitigation strategies for pandemic Influenza in the United States,” Proceedings of the National Academy of Sciences of the United States of America, vol. 103, no. 15, pp. 5935–5940, 2006.
[47]
S. Eubank, H. Guclu, V. S. A. Kumar et al., “Modelling disease outbreaks in realistic urban social networks,” Nature, vol. 429, no. 6988, pp. 180–184, 2004.
[48]
M. E. Halloran, N. M. Ferguson, S. Eubank et al., “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, vol. 105, no. 12, pp. 4639–4644, 2008.
[49]
MIDAS, “Report from the Models of Infectious Disease Agent Study (MIDAS) Steering Committee,” 2004, http://www.nigms.nih.gov/News/Reports/midas_steering_050404.htm.
[50]
Committee on Modeling Community Containment for Pandemic Influenza, “Modeling community containment for pandemic Influenza: a letter report,” 2006, http://www.nap.edu/catalog/11800.html.
[51]
Centers for Disease Control and Prevention (CDC), “Interim pre-pandemic planning guidance: community strategy for pandemic Influenza mitigation in the United States,” 2007, http://www.pandemicflu.gov/professional/community/community_mitigation.pdf.
[52]
M. I. Meltzer, N. J. Cox, and K. Fukuda, “The economic impact of pandemic Influenza in the United States: priorities for intervention,” Emerging Infectious Diseases, vol. 5, no. 5, pp. 659–671, 1999.
[53]
T. Das and A. Savachkin, “A large scale simulation model for assessment of societal risk and development of dynamic mitigation strategies,” IIE Transactions, vol. 40, no. 9, pp. 893–905, 2008.
[54]
Colardo Department of Human Services Division of Mental Health, “Pandemic Influenza: quarantine, isolation and social distancing,” 2009, http://www.flu.gov/news/colorado_toolbox.pdf.
[55]
J. T. Wu, S. Riley, and G. M. Leung, “Spatial considerations for the allocation of pre-pandemic Influenza vaccination in the United States,” Proceedings of the Royal Society B: Biological Sciences, vol. 274, no. 1627, pp. 2811–2817, 2007.
[56]
J. Lawless and J. Lawless, Statistical Models and Methods for Lifetime Data, John Wiley & Sons, New York, NY, USA, 1982.
[57]
O. Diekmann and J. Heesterbeek, Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation, John Wiley & Sons, New York, NY, USA, 2000.
[58]
J. F. Brundage and G. D. Shanks, “Deaths from bacterial pneumonia during 1918-19 Influenza pandemic,” Emerging Infectious Diseases, vol. 14, no. 8, pp. 1193–1199, 2008.
[59]
Centers for Disease Control and Prevention (CDC), “CDC Influenza operational plan,” 2006, http://www.cdc.gov/flu/pandemic/cdcplan.htm.
[60]
World Health Organization (WHO), “WHO guidelines on the use of vaccine and antivirals during Influenza pandemics,” 2004, http://www.who.int/csr/resources/publications/Influenza/11_29_01_A.pdf.
[61]
S. Pasteur, “Influenza A(H1N1) Monovalent Vaccine,” 2009, http://www.fda.gov/downloads/biologicsbloodvaccines/vaccines/approvedproducts/ucm182404.pfd.
[62]
R. J. Blendon, L. M. Koonin, J. M. Benson et al., “Public response to community mitigation measures for pandemic Influenza,” Emerging Infectious Diseases, vol. 14, no. 5, pp. 778–786, 2008.
[63]
M. Z. Sadique, W. J. Edmunds, R. D. Smith et al., “Precautionary behavior in response to perceived threat of pandemic Influenza,” Emerging Infectious Diseases, vol. 13, no. 9, pp. 1307–1313, 2007.
[64]
R. Maunder, J. Hunter, L. Vincent et al., “The immediate psychological and occupational impact of the 2003 SARS outbreak in a teaching hospital,” Canadian Medical Association Journal, vol. 168, no. 10, pp. 1245–1251, 2003.
[65]
E. Robertson, K. Hershenfield, S. L. Grace, and D. E. Stewart, “The psychosocial effects of being quarantined following exposure to SARS: a qualitative study of Toronto health care workers,” Canadian Journal of Psychiatry, vol. 49, no. 6, pp. 403–407, 2004.
[66]
M. Pearson, C. Bridges, and S. Harper, “Influenza vaccination of health-care personnel,” MMWR, vol. 55, no. 2, pp. 1–16, 2006.
[67]
M. T. Keane, M. V. Walter, B. I. Patel et al., “Confidence in vaccination: a parent model,” Vaccine, vol. 23, no. 19, pp. 2486–2493, 2005.
[68]
V. P. Niederhauser, G. Baruffi, and R. Heck, “Parental decision-making for the varicella vaccine,” Journal of Pediatric Health Care, vol. 15, no. 5, pp. 236–243, 2001.
[69]
S. D. Rhodes and K. C. Hergenrather, “Exploring hepatitis B vaccination acceptance among young men who have sex with men: facilitators and barriers,” Preventive Medicine, vol. 35, no. 2, pp. 128–134, 2002.
[70]
S. L. Rosenthal, R. K. Kottenhahn, F. M. Biro, and P. A. Succop, “Hepatitis B vaccine acceptance among adolescents and their parents,” Journal of Adolescent Health, vol. 17, no. 4, pp. 248–254, 1995.
[71]
M. S. Smailbegovic, G. J. Laing, and H. Bedford, “Why do parents decide against immunization? The effect of health beliefs and health professionals,” Child: Care, Health and Development, vol. 29, no. 4, pp. 303–311, 2003.
[72]
T. Safranek, D. Lawrence, L. Kuriand, et al., “Reassessment of the association between Guillain-Barré syndrome and receipt of swine Influenza vaccine in 1976-1977: results of a two-state study,” American Journal of Epidemiology, vol. 133, no. 9, p. 940, 1991.
[73]
K. M. Cummings, A. M. Jette, B. M. Brock, and D. P. Haefner, “Psychosocial determinants of immunization behavior in a swine Influenza campaign,” Medical Care, vol. 17, no. 6, pp. 639–649, 1979.
[74]
The New Yorker, “The fear factor,” 2009, http://www.newyorker.com/talk/comment/2009/10/12/091012taco_talk_specter.
[75]
The New York Times, “Doctors swamped by swine flu vaccine fears,” 2009, http://www.msnbc.msn.com/id/33179695/ns/health-swine_flu/.
[76]
A. Gosavi, T. K. Das, and S. Sarkar, “A simulation based learning automata framework for solving semi-Markov decision problems under long run average reward,” IIE Transactions in Operations Engineering, vol. 36, no. 6, pp. 557–567, 2001.
[77]
A. Savachkin, A. Uribe-Sánchez, T. Das, D. Prieto, A. Santana, and D. Martinez, “Supplemental data and model parameter values for cross-regional simulation-based optimization testbed,” 2010, http://imse.eng.usf.edu/pandemic/supplement.pdf.
[78]
U.S Census Bureau, “2001 American community survey,” 2000, http://www.census.gov/prod/2001pubs/statab/sec01.pdf.
[79]
Bureau of transportation statistics, “2001 National household travel survey (NTHS),” 2002, http://www.bts.gov/programs/national_household_travel_survey/.
[80]
“Tampa International Airport: daily traffic volume data,” 2010, http://www.tampaairport.com.
[81]
“Miami International Airport: daily traffic volume data,” 2010, http://www.miami-airport.com.
[82]
“Miami International Airport: daily traffic volume data,” 2010, http://www.jaa.aero/General/Default.
Writing committee of the World Health Organization (WHO), “Consultation on human Influenza A/H5.Avian Influenza A(H5N1) infection in humans,” The New England Journal of Medicine, vol. 353, no. 13, pp. 1374–1385, 2005.
[86]
Institute of Medicine (IOM), Antivirals for Pandemic Influenza: Guidance on Developing a Distribution and Dispensing Program, The National Academies Press, Washington, DC, USA, 2008.
[87]
J. J. Treanor, J. D. Campbell, K. M. Zangwill, T. Rowe, and M. Wolff, “Safety and immunogenicity of an inactivated subvirion Influenza A (H5N1) vaccine,” The New England Journal of Medicine, vol. 354, no. 13, pp. 1343–1351, 2006.
[88]
R. J. Blendon, C. M. DesRoches, M. S. Cetron, J. M. Benson, T. Meinhardt, and W. Pollard, “Attitudes toward the use of quarantine in a public health emergency in four countries,” Health Affairs, vol. 25, no. 2, pp. 15–25, 2006.
[89]
D. Montgomery, Design and Analysis of Experiments, John Wiley & Sons, New York, NY, USA, 2007.
[90]
T. Halfhill, “Inflation calculator,” 2009, http://www.halfhill.com/inflation.html.
[91]
D. Bell, A. Nicoll, K. Fukuda et al., “Nonpharmaceutical interventions for pandemic Influenza, national and community measures,” Emerging Infectious Diseases, vol. 12, no. 1, pp. 88–94, 2006.
