Author

P'eter L. Simon

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Preprint Oct 2026

Fast-variable reduction to complex contagion unifies epidemic models

Across biological and social complex systems, models of epidemics or contagions incorporate complexity through network correlations, adaptive behavior, higher-order interactions, or co-circulating strains. Tracking these mechanisms lead to high-dimensional mathematical systems that resist analytical treatment. We show...

Laurent Hébert-Dufresne, P'eter L. Simon, István Z. Kiss · 0 citations

Preprint Jul 2026

A principled closure framework for higher-order SIS epidemic models on networks

A bottom-up derivation of higher-order SIS dynamics, building systematically from node-level equations to pairs, triplets, and three-body interactions and provides a principled method of generating new models.

Kevin Teo, Péter L. Simon, I. Z. Kiss · 0 citations

Preprint Jun 2026

Edge-based mean-field approximation of dynamics on networks via approximate lumping of Markov chains

A mathematically principled framework for deriving edge-based mean-field approximations for a broad class of Markov processes on networks using approximate lumping is presented, which yields density-dependent population processes that reduce to a low-dimensional system of ordinary differential equations.

G. Timár, Jonathan A. Ward, Péter L. Simon · 0 citations