Behavior of susceptible-infected-susceptible epidemics on heterogeneous networks with saturation

Abstract

We investigate saturation effects in susceptible-infected-susceptible (SIS) models of the spread of epidemics in heterogeneous populations. The structure of interactions in the population is represented by networks with connectivity distribution $P(k)$,including scale-free(SF) networks with power law distributions $P(k)\sim k^{-\gamma }$. Considering cases where the transmission of infection between nodes depends on their connectivity, we introduce a saturation function $C(k)$ which reduces the infection transmission rate $\lambda$ across an edge going from a node with high connectivity $k$. A mean field approximation with the neglect of degree-degree correlation then leads to a finite threshold ${\lambda }_c>0$ for SF networks with $2<\gamma \le 3$. We also find, in this approximation, the fraction of infected individuals among those with degree $k$ for $\lambda$ close to ${\lambda }_c$. We investigate via computer simulation the contact process on a heterogeneous regular lattice and compare the results with those obtained from mean field theory with and without neglect of degree-degree correlations.

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References in corpus (12)

• Emergence of scaling in random networks
• Statistical mechanics of complex networks
• Epidemic spreading in scale-free networks
• The diameter of the world wide web
• The spread of epidemic disease on networks
• Evolution of networks
• Epidemic dynamics and endemic states in complex networks
• The Web of Human Sexual Contacts
• Topology of evolving networks: local events and universality
• Epidemic dynamics in finite size scale-free networks
• Absence of epidemic threshold in scale-free networks with connectivity correlations
• Epidemic Incidence in Correlated Complex Networks

Cited by in corpus (7)

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• An efficient strategy to suppress epidemic explosion in heterogeneous metapopulation networks
• The Role of Second Trials in Cascades of Information over Networks
• Comparison of mean-field based theoretical analysis methods for SIS model
• Degree dependent transmission rates in epidemic processes
• Predicting epidemics on weighted networks
• Stochastic spreading processes on a network model based on regular graphs