IDEAS home Printed from https://ideas.repec.org/a/spr/stmapp/v23y2014i4p601-646.html
   My bibliography  Save this article

Bayesian hierarchical statistical SIRS models

Author

Listed:
  • Lili Zhuang
  • Noel Cressie

Abstract

The classic susceptible-infectious-recovered (SIR) model, has been used extensively to study the dynamical evolution of an infectious disease in a large population. The SIR-susceptible (SIRS) model is an extension of the SIR model to allow modeling imperfect immunity (those who have recovered might become susceptible again). SIR(S) models assume observed counts are “mass balanced.” Here, mass balance means that total count equals the sum of counts of the individual components of the model. However, since the observed counts have errors, we propose a model that assigns the mass balance to the hidden process of a (Bayesian) hierarchical SIRS (HSIRS) model. Another challenge is to capture the stochastic or random nature of an epidemic process in a SIRS. The HSIRS model accomplishes this through modeling the dynamical evolution on a transformed scale. Through simulation, we compare the HSIRS model to the classic SIRS model, a model where it is assumed that the observed counts are mass balanced and the dynamical evolution is deterministic. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Lili Zhuang & Noel Cressie, 2014. "Bayesian hierarchical statistical SIRS models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(4), pages 601-646, November.
    • Handle: RePEc:spr:stmapp:v:23:y:2014:i:4:p:601-646
    DOI: 10.1007/s10260-014-0280-9
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10260-014-0280-9
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10260-014-0280-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    2. Julian Besag & Jeremy York & Annie Mollié, 1991. "Bayesian image restoration, with two applications in spatial statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(1), pages 1-20, March.
    3. Vanja Dukic & Hedibert F. Lopes & Nicholas G. Polson, 2012. "Tracking Epidemics With Google Flu Trends Data and a State-Space SEIR Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1410-1426, December.
    4. Jacob Oleson & Christopher Wikle, 2013. "Predicting infectious disease outbreak risk via migratory waterfowl vectors," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(3), pages 656-673.
    5. David A Rasmussen & Oliver Ratmann & Katia Koelle, 2011. "Inference for Nonlinear Epidemiological Models Using Genealogies and Time Series," PLOS Computational Biology, Public Library of Science, vol. 7(8), pages 1-11, August.
    6. Simon N. Wood, 2010. "Statistical inference for noisy nonlinear ecological dynamic systems," Nature, Nature, vol. 466(7310), pages 1102-1104, August.
    7. Aaron A. King & Edward L. Ionides & Mercedes Pascual & Menno J. Bouma, 2008. "Inapparent infections and cholera dynamics," Nature, Nature, vol. 454(7206), pages 877-880, August.
    8. Hooten, Mevin B. & Wikle, Christopher K., 2010. "Statistical Agent-Based Models for Discrete Spatio-Temporal Systems," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 236-248.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zhang, Ping & Wang, Jianwen & Atkinson, Peter M., 2019. "Identifying the spatio-temporal risk variability of avian influenza A H7N9 in China," Ecological Modelling, Elsevier, vol. 414(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wan Yang & Alicia Karspeck & Jeffrey Shaman, 2014. "Comparison of Filtering Methods for the Modeling and Retrospective Forecasting of Influenza Epidemics," PLOS Computational Biology, Public Library of Science, vol. 10(4), pages 1-15, April.
    2. King, Aaron A. & Lin, Qianying & Ionides, Edward L., 2022. "Markov genealogy processes," Theoretical Population Biology, Elsevier, vol. 143(C), pages 77-91.
    3. Ross, J.V. & Pagendam, D.E. & Pollett, P.K., 2009. "On parameter estimation in population models II: Multi-dimensional processes and transient dynamics," Theoretical Population Biology, Elsevier, vol. 75(2), pages 123-132.
    4. Katie Wilson & Jon Wakefield, 2022. "A probabilistic model for analyzing summary birth history data," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 47(11), pages 291-344.
    5. Grazzini, Jakob & Richiardi, Matteo G. & Tsionas, Mike, 2017. "Bayesian estimation of agent-based models," Journal of Economic Dynamics and Control, Elsevier, vol. 77(C), pages 26-47.
    6. Eibich, Peter & Ziebarth, Nicolas, 2014. "Examining the Structure of Spatial Health Effects in Germany Using Hierarchical Bayes Models," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 49, pages 305-320.
    7. Lahrouz, A. & El Mahjour, H. & Settati, A. & Bernoussi, A., 2018. "Dynamics and optimal control of a non-linear epidemic model with relapse and cure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 299-317.
    8. Christoph Zimmer & Reza Yaesoubi & Ted Cohen, 2017. "A Likelihood Approach for Real-Time Calibration of Stochastic Compartmental Epidemic Models," PLOS Computational Biology, Public Library of Science, vol. 13(1), pages 1-21, January.
    9. Courgeau, Daniel, 2012. "Probability and social science : methodologial relationships between the two approaches ?," MPRA Paper 43102, University Library of Munich, Germany.
    10. Shreosi Sanyal & Thierry Rochereau & Cara Nichole Maesano & Laure Com-Ruelle & Isabella Annesi-Maesano, 2018. "Long-Term Effect of Outdoor Air Pollution on Mortality and Morbidity: A 12-Year Follow-Up Study for Metropolitan France," IJERPH, MDPI, vol. 15(11), pages 1-8, November.
    11. Mayer Alvo & Jingrui Mu, 2023. "COVID-19 Data Analysis Using Bayesian Models and Nonparametric Geostatistical Models," Mathematics, MDPI, vol. 11(6), pages 1-13, March.
    12. Gil, Guilherme Dôco Roberti & Costa, Marcelo Azevedo & Lopes, Ana Lúcia Miranda & Mayrink, Vinícius Diniz, 2017. "Spatial statistical methods applied to the 2015 Brazilian energy distribution benchmarking model: Accounting for unobserved determinants of inefficiencies," Energy Economics, Elsevier, vol. 64(C), pages 373-383.
    13. Andrew Hoegh & Frank T. Manen & Mark Haroldson, 2021. "Agent-Based Models for Collective Animal Movement: Proximity-Induced State Switching," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(4), pages 560-579, December.
    14. Vanessa Santos-Sánchez & Juan Antonio Córdoba-Doña & Javier García-Pérez & Antonio Escolar-Pujolar & Lucia Pozzi & Rebeca Ramis, 2020. "Cancer Mortality and Deprivation in the Proximity of Polluting Industrial Facilities in an Industrial Region of Spain," IJERPH, MDPI, vol. 17(6), pages 1-15, March.
    15. Berti, Patrizia & Dreassi, Emanuela & Rigo, Pietro, 2014. "Compatibility results for conditional distributions," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 190-203.
    16. Louise Choo & Stephen G. Walker, 2008. "A new approach to investigating spatial variations of disease," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 171(2), pages 395-405, April.
    17. Young‐Geun Choi & Lawrence P. Hanrahan & Derek Norton & Ying‐Qi Zhao, 2022. "Simultaneous spatial smoothing and outlier detection using penalized regression, with application to childhood obesity surveillance from electronic health records," Biometrics, The International Biometric Society, vol. 78(1), pages 324-336, March.
    18. Gael M. Martin & David T. Frazier & Christian P. Robert, 2020. "Computing Bayes: Bayesian Computation from 1763 to the 21st Century," Monash Econometrics and Business Statistics Working Papers 14/20, Monash University, Department of Econometrics and Business Statistics.
    19. Zhengyi Zhou & David S. Matteson & Dawn B. Woodard & Shane G. Henderson & Athanasios C. Micheas, 2015. "A Spatio-Temporal Point Process Model for Ambulance Demand," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 6-15, March.
    20. Eric C. Tassone & Marie Lynn Miranda & Alan E. Gelfand, 2010. "Disaggregated spatial modelling for areal unit categorical data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(1), pages 175-190, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:stmapp:v:23:y:2014:i:4:p:601-646. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.