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Bayesian hierarchical statistical SIRS models

Journal Article


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.

Publication Date


  • 2014

Citation


  • Zhuang, L. & Cressie, N. A. (2014). Bayesian hierarchical statistical SIRS models. Statistical Methods and Applications, 23 (4), 601-646.

Scopus Eid


  • 2-s2.0-84912012734

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/4046

Number Of Pages


  • 45

Start Page


  • 601

End Page


  • 646

Volume


  • 23

Issue


  • 4

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.

Publication Date


  • 2014

Citation


  • Zhuang, L. & Cressie, N. A. (2014). Bayesian hierarchical statistical SIRS models. Statistical Methods and Applications, 23 (4), 601-646.

Scopus Eid


  • 2-s2.0-84912012734

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/4046

Number Of Pages


  • 45

Start Page


  • 601

End Page


  • 646

Volume


  • 23

Issue


  • 4