Stochastic simplicial contagion model

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.
D.H.S. is supported by Grant PID2021-128665NB-I00 funded by MCIN/AEI/ 10.13039/501100011033 and, as appropriate, by \ERDF A way of making Eu- rope", Ministerio de Econom a y Competitividad (Spain) under grant MTM2017- 86042-P, the project STAMGAD 18.J445 / 463AC03 by Consejer a de Edu- caci on (GIR, Junta de Castilla y Le on, Spain) and by Universidad de Sala- manca (Spain) under project PIC2-2021-10. J.H.S. is supported by the Span- ish Ministry of Science and Education under the project TCO-RISEBLOCK (PID2019-110224RB-I00), the European Union's H2020 Research and Innova- tion Programme under the Grant Agreement No. 871754 (i3-MARKET), and the Generalitat de Catalunya grant 2017-SGR-00782.
Postprint (author's final draft)