Stochastic simplicial contagion model

Daniel Hernández Serrano, Javier Villarroel, Juan Hernández-Serrano and Ángel Tocino

Chaos, Solitons & Fractals, 2023, vol. 167, issue C

Abstract: We propose a stochastic model that describes of epidemics over simplicial complex networks (SSCM) in which higher-order unforeseen or random interactions may occur. Its dynamics obeys a stochastic differential equation (SDE) based on the mean field approach of the simplicial social contagion model. In this stochastic regime the only possible equilibrium state is the origin. We give conditions to guarantee global stability and hence that the disease dies out. We partition the parameter space into the instability, the bi-stability and the globally asymptotically stable regions described in terms of appropriate epidemiological parameters. These regimes codify whether the disease will, can or will not disappear. We also present empirical results obtained by running different simulations of the SSCM over several real-world simplicial networks and over a synthetically generated one, which validate the theoretical results presented.

Keywords: Complex networks; Simplicial complexes; Mathematical epidemiology; Contagion models; Stochastic differential systems; Stochastic stability; SIS model; Basic reproductive number (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:167:y:2023:i:c:s0960077922011870

DOI: 10.1016/j.chaos.2022.113008

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