2022/08/16 by István Z. Kiss, Kiss, Istvan Z., Eben Kenah +3
Medicine · Physics and Astronomy · Psychology · #60F #60G (Secondary) #92D30 (Primary) #Complex Network Analysis Techniques #FOS: Biological sciences #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Mental Health Research Topics #Populations and Evolution (q-bio.PE) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2208.07983
openalex publication_date 2022/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that the exact closure of SIR pairwise epidemic equations on a configuration model network is possible if and only if the degree distribution is Poisson, Binomial, or Negative Binomial. The proof relies on establishing, for these specific degree distributions, the equivalence of the closed pairwise model and the so-called dynamical survival analysis (DSA) edge-based model which was previously shown to be exact. Indeed, as we show here, the DSA model is equivalent to the well-known edge-based Volz model. We use this result to provide reductions of the closed pairwise and Volz models to the same single equation involving only susceptibles, which has a useful statistical interpretation in terms of the times to infection. We illustrate our findings with some numerical examples.