Epidemic spreading in a variety of scale free networks

Abstract

We have shown that the epidemic spreading in scale-free networks is very sensitive to the statistics of degree distribution characterized by the index gamma, the effective spreading rate lambda, the social strategy used by individuals to choose a partner, and the policy of administrating a cure to an infected node. Depending on the interplay of these four factors, the stationary fractions of infected population F(gamma) as well as the epidemic threshold properties can be essentially different. We have given an example of the evolutionary scale-free network which is disposed to the spreading and the persistence of infections at any spreading rate lambda>0 for any gamma. Probably, it is impossible to obtain a simple immunization program that can be simultaneously effective for all types of scale-free networks. We have also studied the dynamical solutions for the evolution equation governed by the epidemic spreading in scale-free networks and found that for the case of vanishingly small cure rate delta<<1 the initial configuration of infected nodes would feature the solution for very long times.

The spread of infectious disease on complex networks with household-structure

“…So the epidemic threshold is determined by three parameters(N, β, γ) and the networks degree distribution p(k). We notice that the expression (23) involves multiplication of the well-known term k k 2 [2,4,6,9], which is closely related to the "average" number of secondary infections [7,8]. Not surprising, this result is the same as that of the standard SIS model [4].…”

“…The dynamical behavior of so-called susceptibleinfected-susceptible (SIS) model and susceptible-infected-removed (SIR) model have been widely investigated on regular network and complex networks [1][2][3][4][5][6][7][8][9][10][11][12]. Within the studying, individuals are modeled as sites and possible contacts between individuals are linked by edges between the sites.…”

Complex networks: Structure and dynamics

“…Another interesting contribution to the topic comes from Volchenkov et al, who introduced a network model having scale-free properties and showing persistent infections at any spreading rate > 0 and for any > 1 [367]. Such alternative flexible model is inspired by the principle of evolutionary selection of common large-scale structure in biological networks.…”

Nonlinear Diffusion Through Large Complex Networks Containing Regular Subgraphs

“…Our approach to the complex networks containing large well-structured regular subgraphs could be used in studies of spreading of viruses [41] or social epidemics [42], traffic properties and modelling of various ecological webs.…”