In this paper we study the diffusion of an SIS-type epidemics on a network under the presence of a random environment, that enters in the definition of the infection rates of the nodes. Accordingly, we model the infection rates in the form of independent stochastic processes. To analyze the problem, we apply a mean field approximation, which allows to get a stochastic differential equations for the probability of infection in each node, and classical tools about stability, which require to find suitable Lyapunov's functions. Here, we find conditions which guarantee, respectively, extinction and stochastic persistence of the epidemics. We show that there exists two regions, given in terms of the coefficients of the model, one where the system goes to extinction almost surely, and the other where it is stochastic permanent. These two regions are, unfortunately, not adjacent, as there is a gap between them, whose extension depends on the specific level of noise. In this last region, we perform numerical analysis to suggest the true behavior of the solution.

Epidemics on networks with heterogeneous population and stochastic infection rates / Bonaccorsi, Stefano; Ottaviano, Stefania. - In: MATHEMATICAL BIOSCIENCES. - ISSN 0025-5564. - 2016, 279:(2016), pp. 43-52. [10.1016/j.mbs.2016.07.002]

Epidemics on networks with heterogeneous population and stochastic infection rates

Bonaccorsi, Stefano;Ottaviano, Stefania
2016

Abstract

In this paper we study the diffusion of an SIS-type epidemics on a network under the presence of a random environment, that enters in the definition of the infection rates of the nodes. Accordingly, we model the infection rates in the form of independent stochastic processes. To analyze the problem, we apply a mean field approximation, which allows to get a stochastic differential equations for the probability of infection in each node, and classical tools about stability, which require to find suitable Lyapunov's functions. Here, we find conditions which guarantee, respectively, extinction and stochastic persistence of the epidemics. We show that there exists two regions, given in terms of the coefficients of the model, one where the system goes to extinction almost surely, and the other where it is stochastic permanent. These two regions are, unfortunately, not adjacent, as there is a gap between them, whose extension depends on the specific level of noise. In this last region, we perform numerical analysis to suggest the true behavior of the solution.
Bonaccorsi, Stefano; Ottaviano, Stefania
Epidemics on networks with heterogeneous population and stochastic infection rates / Bonaccorsi, Stefano; Ottaviano, Stefania. - In: MATHEMATICAL BIOSCIENCES. - ISSN 0025-5564. - 2016, 279:(2016), pp. 43-52. [10.1016/j.mbs.2016.07.002]
File in questo prodotto:
File Dimensione Formato  
MathBioPersitenza.pdf

accesso aperto

Descrizione: Preprint submitted to Elsevier, July 20, 2016
Tipologia: Pre-print non referato (Non-refereed preprint)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 163.86 kB
Formato Adobe PDF
163.86 kB Adobe PDF Visualizza/Apri
1-s2.0-S0025556416300840-main.pdf

Solo gestori archivio

Tipologia: Versione editoriale (Publisher’s layout)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 1.07 MB
Formato Adobe PDF
1.07 MB Adobe PDF   Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11572/152320
Citazioni
  • ???jsp.display-item.citation.pmc??? 0
  • Scopus 7
  • ???jsp.display-item.citation.isi??? 5
social impact