Autor(es)

Rodriguez, Pablo M. ; Roldan-Correa, Alejandro ; Alexander Valencia, Leon

• Tipo de documento: Artigo Científico
• Fonte: PHYSICAL REVIEW E; v. 98, n. 2, p. 4-pg., 2018-08-03.

Resumo

Cator and Van Mieghem [Phys.Rev.E 89, 052802 (2014)] stated that the correlation of infection at the same time between any pair of nodes in a network is non-negative for the Markovian susceptible-infected-susceptible (SIS) and susceptible-infected-removed (SIR) epidemic models. The arguments used to obtain this result rely strongly on the graphical construction of the stochastic process, as well as the Fortuin, Kasteleyn, and Ginibre (FKG) inequality. In this Comment, we show that although the approach used by the authors applies to the SIS model, it cannot be used for the SIR model as stated in their work. In particular, we observe that monotonicity in the process is crucial for invoking the FKG inequality. Moreover, we provide an example of a simple graph for which the nodal infection in the SIR Markovian model is negatively correlated. (AU)

• Processo FAPESP: 16/11648-0 - Teoremas limite e resultados de transição de fase para modelos de propagação de informação em grafos
• Beneficiário: Pablo Martin Rodriguez
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 17/10555-0 - Modelagem estocástica de sistemas interagentes
• Beneficiário: Fabio Prates Machado
• Modalidade de apoio: Auxílio à Pesquisa - Temático