A stochastic simplicial SIS model driven by two independent noises

• Ángel Tocino ^[1] ; Juan Hernández-Serrano ^[2] ; Daniel Hernández Serrano ^[1]
  1. [1] Universidad de Salamanca

     Universidad de Salamanca

     Salamanca, España

     
  2. [2] Universitat Polit`ecnica de Catalunya, Barcelona, Spain
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 69, Nº. 1, 2026, págs. 227-246
• Idioma: inglés
• DOI: 10.33044/revuma.4994
• Enlaces
  • Texto completo
• Resumen

  • We propose a stochastic simplicial SIS model where two independent sources of noise are utilized to perturb the individual and collective infection rates. After proving that the model has a unique global solution, two sets of conditions on the parameters that give exponential stability of the trivial solution are presented. We then find conditions for persistence and show that the solution of the SDE oscillates infinitely often around a point under such requirements. We validate the theoretical statements by performing numerical experiments, as well as simulations on both real and synthetic simplicial networks, with results that align with the theoretical and numerical predictions of the model.

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