Effects of the distance among multiple spreaders on the spreading

It is very important to investigate the multiple spreaders' effects since the spreading phenomenon is ubiquitous in many complex systems. In this letter, we investigate the effects of the distance among the initial multiple spreaders for regular networks and WS (Watts-Strogatz) small-world networks based on the SIR (Susceptible-Infected-Recovered) model. Assuming the epidemics can spread over the network, the theoretical and experimental results show that for regular networks the larger the distance between spreaders is, the more effective the spreading is. For WS networks, the spreading efficiency will decrease when the distance exceeds a certain value, and a larger connection probability and average degree will result in a smaller distance of the most effective spreading. A better spreading strategy using n spreaders is to choose either the highest k or ks nodes with the condition that there are not any pairs of the n spreaders linked directly (Kitsak M. et al., Nat. Phys., 6 (2010) 888). However, we find that the spreading will be more effective when the distances among the largest-degree spreaders increase. All these results are independent of the network size for the two initial spreaders case. This work may give new insights to explore more effective methods to inhibit the epidemic spreading or increase the information diffusion.