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Bayesian hierarchical statistical SIRS models

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  • 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
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    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).

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