Critical properties of the contact process on a scale-free homophilic network

Abstract

. Using the contact process model within a Monte Carlo numerical simulation approach, we mimic an epidemic spreading on a homophilic network, a scale-free network displaying a small world effect, to show a continuous phase transition to an absorbing-state at a critical threshold . Since the connection number k of the vertices’ homophilic network is cumulative, the degree distribution exhibits, for a large value of networks, a power-law behavior according to , with the distribution exponent . A finite-size scaling analysis allows us to characterize the transition by a set of critical exponents , , β and , whose universality class indicates a disagreement with those associated to the CP on scale-free networks in terms of the heterogeneous mean-field theory.

Critical properties of the SIS model on the clustered homophilic network

“…Numerical simulations in regular networks have shown that the phase transition between active and inactive regimes belongs to the directed percolation universality class [10] . A previous study of the contact process (CP) model on the homophilic network unveiled that the numerical values of the critical exponents, obtained from the heterogeneous mean-field theory and from a standard scale-free network model, were different from those found on the homophilic one [11] .…”

“…In addition, more attention has been devoted to the study of social [22] , cultural phenomena and the spread of viruses on computers [23] , and epidemic diseases [19] , [20] in complex networks. Recently, the CP and SIS models were shown to share the same universality class in the deterministic Apollonian network [11] , [19] , [20] , while the former model in the homophilic network exhibited a phase transition [11] . Pastor-Satorras [12] , [13] showed that there was no phase transition in the SIS model in a random scale-free network model.…”

Modified Epidemic Diffusive Process on the Apollonian Network

“…The Contact Process (CP) model [12][13][14][15], Diffusive Epidemic Process (DEP) model [16][17][18][19][20], among others.…”

Dinâmica estocástica de populações biológicas

“…Investigouse o modelo suscetível-infectado-suscetível (SIS) por diferentes ângulos, por exemplo, comparou-se resultados teóricos e de simulações numéricas [70], fez-se investigações em redes aleatórias livres de escalas [71]. O processo de contato (que equivale ao SIS em redes regulares) também foi estudado de diversas formas, por exemplo, investigou-se o comportamento crítico em redes do tipo "small world" [72], em junções tipo estrela [73] e em uma rede livre escala de homofílica [74]. Redes complexas também foram utilizadas para representar metapopulações [75] no estudo dos efeitos de estruturas de populações locais.…”

“…74) em que = λ − λ c e f , g e j são funções universais. Das leis de escalas notamos que podemos utilizar o cruzamento da grandeza u para determinar o ponto 5.3.…”