  In this paper, we focus on the node-based epidemic modeling for networks,
introduce the propagation medium and propose a node-based
Susceptible-Infected-Recovered-Susceptible (SIRS) epidemic model with infective
media. Theoretical investigations show that the endemic equilibrium is globally
asymptotically stable. Numerical examples of three typical network structures
also verify the theoretical results. Furthermore, Comparison between network
node degree and its infected percents implies that there is a strong positive
correlation between both, namely, the node with bigger degree is infected with
more percents. Finally, we discuss the impact of the epidemic spreading rate of
media as well as the effective recovered rate on the network average infected
state. Theoretical and numerical results show that (1) network average infected
percents go up (down) with the increase of the infected rate of media (the
effective recovered rate); (2) the infected rate of media has almost no
influence on network average infected percents for the fully-connected network
and NW small-world network; (3) network average infected percents decrease
exponentially with the increase of the effective recovered rate, implying that
the percents can be controlled at low level by an appropriate large effective
recovered rate.
