## DIMACS TR: 2004-14

##
Behavior of $SIS$ epidemics on heterogeneous networks with saturation

### Authors: Jaewook Joo and Joel Lebowitz

**
ABSTRACT
**
We investigate saturation effects in susceptible-infected-susceptible (SIS) mode
ls 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 t
heir connectivity, we introduce a saturation function $C(k)$ which reduces the i
nfection transmission rate $\lambda$ across an edge going from a node with high
connectivity $k$. A mean field approximation with the neglect of degree-degree c
orrelation 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.

Paper Available at:
ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2004/2004-14.ps.gz

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