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In this paper, we focus on the node-based epidemic modeling for networks,introduce the propagation medium and propose a node-basedSusceptible-Infected-Recovered-Susceptible (SIRS) epidemic model with infectivemedia. Theoretical investigations show that the endemic equilibrium is globallyasymptotically stable. Numerical examples of three typical network structuresalso verify the theoretical results. Furthermore, Comparison between networknode degree and its infected percents implies that there is a strong positivecorrelation between both, namely, the node with bigger degree is infected withmore percents. Finally, we discuss the impact of the epidemic spreading rate ofmedia as well as the effective recovered rate on the network average infectedstate. Theoretical and numerical results show that (1) network average infectedpercents go up (down) with the increase of the infected rate of media (theeffective recovered rate); (2) the infected rate of media has almost noinfluence on network average infected percents for the fully-connected networkand NW small-world network; (3) network average infected percents decreaseexponentially with the increase of the effective recovered rate, implying thatthe percents can be controlled at low level by an appropriate large effectiverecovered rate.

A node-based SIRS epidemic model with infective media on complex networks