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

Jaewook Joo·Joel L. Lebowitz
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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 $P(k)\sim k^{-γ}$. 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 $λ$ 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 $λ_{c}>0$ for SF networks with $2<γ\leq 3$. We also find, in this approximation, the fraction of infected individuals among those with degree $k$ for $λ$ close to $λ_{c}$. 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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Jaewook Joo, Joel L. Lebowitz. 2004-04-24. Behavior of susceptible-infected-susceptible epidemics on heterogeneous networks with saturation. https://doi.org/10.1103/physreve.69.066105

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