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

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

2004-02-03

arxiv.org/abs/cond-mat/0402065v2

Phys. Rev. E, 69 (2004) 066105

Physics

Condensed Matter

Statistical Mechanics

6 figures

Scientific paper

10.1103/PhysRevE.69.066105

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 $2<\gamma \leq 3$. 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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