Necessary and sufficient conditions for exact closures of epidemic equations on configuration model networks.
J Math Biol
; 87(2): 36, 2023 08 02.
Article
en En
| MEDLINE
| ID: mdl-37532967
ABSTRACT
We prove that it is possible to obtain the exact closure of SIR pairwise epidemic equations on a configuration model network if and only if the degree distribution follows a Poisson, binomial, or negative binomial distribution. The proof relies on establishing the equivalence, for these specific degree distributions, between the closed pairwise model and a dynamical survival analysis (DSA) model that was previously shown to be exact. Specifically, we demonstrate that the DSA model is equivalent to the well-known edge-based Volz model. Using this result, we also provide reductions of the closed pairwise and Volz models to a single equation that involves only susceptibles. This equation has a useful statistical interpretation in terms of times to infection. We provide some numerical examples to illustrate our results.
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Bases de datos:
MEDLINE
Asunto principal:
Enfermedades Transmisibles
/
Epidemias
Límite:
Humans
Idioma:
En
Revista:
J Math Biol
Año:
2023
Tipo del documento:
Article
País de afiliación:
Reino Unido