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Simple Models of Influenza Progression Within a Heterogeneous Population

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  • Richard C. Larson

    (Center for Engineering Systems Fundamentals, Engineering Systems Division, and Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

Abstract

The focus of this “OR framing paper” is to introduce the operations research (OR) community to the need for new mathematical modeling of an influenza pandemic and its control. By reviewing relevant history and literature, one key concern that emerges relates to how a population’s heterogeneity may affect disease progression. Another is to explore within a modeling framework “social distancing” as a disease progression control method, where social distancing refers to steps aimed at reducing the frequency and intensity of daily human-to-human contacts. To depict social contact behavior of a heterogeneous population susceptible to infection, a nonhomogeneous probabilistic mixing model is developed. Partitioning the population of susceptibles into subgroups, based on frequency of daily human contacts and infection propensities, a stylistic difference equation model is then developed depicting the day-to-day evolution of the disease. This simple model is then used to develop a preliminary set of results. Two key findings are (1) early exponential growth of the disease may be dominated by susceptibles with high human contact frequencies and may not be indicative of the general population’s susceptibility to the disease, and (2) social distancing may be an effective nonmedical way to limit and perhaps even eradicate the disease. Much more decision-focused research needs to be done before any of these preliminary findings may be used in practice.

Suggested Citation

  • Richard C. Larson, 2007. "Simple Models of Influenza Progression Within a Heterogeneous Population," Operations Research, INFORMS, vol. 55(3), pages 399-412, June.
  • Handle: RePEc:inm:oropre:v:55:y:2007:i:3:p:399-412
    DOI: 10.1287/opre.1070.0399
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    References listed on IDEAS

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    1. Helen J Wearing & Pejman Rohani & Matt J Keeling, 2005. "Appropriate Models for the Management of Infectious Diseases," PLOS Medicine, Public Library of Science, vol. 2(7), pages 1-1, July.
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    Cited by:

    1. Savachkin, Alex & Uribe, Andrés, 2012. "Dynamic redistribution of mitigation resources during influenza pandemics," Socio-Economic Planning Sciences, Elsevier, vol. 46(1), pages 33-45.
    2. Osman Y. Özaltın & Oleg A. Prokopyev & Andrew J. Schaefer & Mark S. Roberts, 2011. "Optimizing the Societal Benefits of the Annual Influenza Vaccine: A Stochastic Programming Approach," Operations Research, INFORMS, vol. 59(5), pages 1131-1143, October.
    3. Teytelman, Anna & Larson, Richard C., 2012. "Modeling influenza progression within a continuous-attribute heterogeneous population," European Journal of Operational Research, Elsevier, vol. 220(1), pages 238-250.
    4. Yaesoubi, Reza & Cohen, Ted, 2011. "Generalized Markov models of infectious disease spread: A novel framework for developing dynamic health policies," European Journal of Operational Research, Elsevier, vol. 215(3), pages 679-687, December.
    5. Duijzer, Lotty Evertje & van Jaarsveld, Willem & Dekker, Rommert, 2018. "Literature review: The vaccine supply chain," European Journal of Operational Research, Elsevier, vol. 268(1), pages 174-192.
    6. Nigmatulina, Karima R. & Larson, Richard C., 2009. "Living with influenza: Impacts of government imposed and voluntarily selected interventions," European Journal of Operational Research, Elsevier, vol. 195(2), pages 613-627, June.
    7. Guihua Wang, 2022. "Stay at home to stay safe: Effectiveness of stay‐at‐home orders in containing the COVID‐19 pandemic," Production and Operations Management, Production and Operations Management Society, vol. 31(5), pages 2289-2305, May.
    8. Rezapour, Shabnam & Baghaian, Atefe & Naderi, Nazanin & Sarmiento, Juan P., 2023. "Infection transmission and prevention in metropolises with heterogeneous and dynamic populations," European Journal of Operational Research, Elsevier, vol. 304(1), pages 113-138.
    9. Xiaoyan Xu & Suresh P. Sethi & Sai‐Ho Chung & Tsan‐Ming Choi, 2023. "Reforming global supply chain management under pandemics: The GREAT‐3Rs framework," Production and Operations Management, Production and Operations Management Society, vol. 32(2), pages 524-546, February.
    10. Firas Rifai, 2018. "Transfer of Knowhow and Experiences from Commercial Logistics into Humanitarian Logistics to Improve Rescue Missions in Disaster Areas," Journal of Management and Sustainability, Canadian Center of Science and Education, vol. 8(3), pages 1-63, August.
    11. Duijzer, Lotty Evertje & van Jaarsveld, Willem & Dekker, Rommert, 2018. "The benefits of combining early aspecific vaccination with later specific vaccination," European Journal of Operational Research, Elsevier, vol. 271(2), pages 606-619.
    12. Rachael M. Jones & Elodie Adida, 2013. "Selecting Nonpharmaceutical Interventions for Influenza," Risk Analysis, John Wiley & Sons, vol. 33(8), pages 1473-1488, August.
    13. Ozgur M. Araz & Mayteé Cruz-Aponte & Fernando A. Wilson & Brock W. Hanisch & Ruth S. Margalit, 2022. "An Analytic Framework for Effective Public Health Program Design Using Correctional Facilities," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 113-128, January.
    14. Naveed Chehrazi & Lauren E. Cipriano & Eva A. Enns, 2019. "Dynamics of Drug Resistance: Optimal Control of an Infectious Disease," Operations Research, INFORMS, vol. 67(3), pages 619-650, May.
    15. Yarmand, Hamed & Ivy, Julie S. & Denton, Brian & Lloyd, Alun L., 2014. "Optimal two-phase vaccine allocation to geographically different regions under uncertainty," European Journal of Operational Research, Elsevier, vol. 233(1), pages 208-219.
    16. Ali Ekici & Pınar Keskinocak & Julie L. Swann, 2014. "Modeling Influenza Pandemic and Planning Food Distribution," Manufacturing & Service Operations Management, INFORMS, vol. 16(1), pages 11-27, February.
    17. Zhang, Jianghua & Long, Daniel Zhuoyu & Li, Yuchen, 2023. "A reliable emergency logistics network for COVID-19 considering the uncertain time-varying demands," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 172(C).

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