A Note on the Markovian SIR Epidemic on a Random Graph with Given Degrees

Malwina Luczak ()
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Malwina Luczak: The University of Manchester

Journal of Theoretical Probability, 2024, vol. 37, issue 2, 1039-1051

Abstract: Abstract We consider a Markovian model of an SIR epidemic spreading on a contact graph that is drawn uniformly at random from the set of all graphs with n vertices and given vertex degrees. Janson, Luczak and Windridge (Random Struct Alg 45(4):724–761, 2014) prove that the evolution of such an epidemic is well approximated by the solution to a simple set of differential equations, thus providing probabilistic underpinnings to the works of Miller (J Math Biol 62(3):349–358, 2011) and Volz (J Math Biol 56(3):293–310, 2008). The present paper provides an additional probabilistic interpretation of the limiting deterministic functions in Janson, Luczak and Windridge (Random Struct Alg 45(4):724–761, 2014), thus clarifying further the connection between their results and the results of Miller and Volz.

Keywords: SIR epidemic process; Random graph with given degree sequence; Configuration model; 05C80; 60F99; 60J28; 92D30 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10959-024-01320-w

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