Skip to main content
Bayesian hierarchical statistical SIRS models
Faculty of Engineering and Information Sciences - Papers
  • Lili Zhuang, Ohio State University
  • Noel A Cressie, University of Wollongong
Publication Date
Publication Details

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


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.

Citation Information
Lili Zhuang and Noel A Cressie. "Bayesian hierarchical statistical SIRS models" (2014)
Available at: