2011/06/30 by Joel C. Miller, Erik Volz, Erik M. Volz
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · Physics and Astronomy · #Action (physics) #Applied mathematics #COVID-19 epidemiological studies #Complex Network Analysis Techniques #Computer science #Convergence (economics) #Epidemic model #Hierarchy #Mathematical and Theoretical Epidemiology and Ecology Models #Mathematical optimization #Mathematics #Physics #Population #Population model #physics.bio-ph #q-bio.PE
paper · pdf · doi:10.1007/s00285-012-0572-3
published as Journal of Mathematical Biology October 2013, Volume 67, Issue 4, pp 869-899
arxiv created 2011/06/30 · openalex publication_date 2012/08/21 · arxiv updated 2015/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We consider the edge-based compartmental models for epidemic spread developed in Part I. We show conditions under which simpler models may be substituted for more detailed models, and in so doing we define a hierarchy of epidemic models. In particular we provide conditions under which it is appropriate to use the standard mass action SIR model, and we show what happens when these conditions fail. Using our hierarchy, we provide a procedure leading to the choice of the appropriate model for a given population. Our result about the convergence of models to the Mass Action model gives clear, rigorous conditions under which the Mass Action model is accurate.