Theoretical Ecology

, Volume 6, Issue 4, pp 457–473 | Cite as

Multi-species SIR models from a dynamical Bayesian perspective

  • Lili ZhuangEmail author
  • Noel Cressie
  • Laura Pomeroy
  • Daniel Janies
Original Paper


Multi-species compartment epidemic models, such as the multi-species susceptible–infectious–recovered (SIR) model, are extensions of the classic SIR models, which are used to explore the transient dynamics of pathogens that infect multiple hosts in a large population. In this article, we propose a dynamical Bayesian hierarchical SIR (HSIR) model, to capture the stochastic or random nature of an epidemic process in a multi-species SIR (with recovered becoming susceptible again) dynamical setting, under hidden mass balance constraints. We call this a Bayesian hierarchical multi-species SIR (MSIRB) model. Different from a classic multi-species SIR model (which we call MSIRC), our approach imposes mass balance on the underlying true counts rather than, improperly, on the noisy observations. Moreover, the MSIRB model can capture the discrete nature of, as well as uncertainties in, the epidemic process.


Mass balance Epidemic model Influenza HSIR MSIR Disease dynamics 



We would like to express our appreciation to the referees and the editor for their constructive comments, which led to important improvements. Cressie’s research was partially supported by the Naval Surface Warfare Center, Dahlgren Division, under grant number N00178-10-Q-3903. We acknowledge that this material is based upon work supported by, or in part by, the US Army Research Laboratory and Office under grant number W911NF-05-1-0271.


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Lili Zhuang
    • 1
    Email author
  • Noel Cressie
    • 2
  • Laura Pomeroy
    • 3
  • Daniel Janies
    • 4
  1. 1.Department of StatisticsThe Ohio State UniversityColumbusUSA
  2. 2.NIASRA, School of Mathematics and Applied StatisticsUniversity of WollongongWollongongAustralia
  3. 3.College of Veterinary MedicineThe Ohio State UniversityColumbusUSA
  4. 4.Department of Bioinformatics and GenomicsUniversity of North Carolina at CharlotteCharlotteUSA

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