Epidemic spreading by objective traveling

A fundamental feature of agent traveling in social networks is that traveling is usually not a random walk but with a specific destination and goes through the shortest path from starting to destination. A serious consequence of the objective traveling is that it may result in a fast epidemic spreading, such as SARS etc. In this letter we present a reaction-traveling model to study how the objective traveling influences the epidemic spreading. We consider a random scale-free meta-population network with sub-population at each node. Through a SIS model we theoretically prove that near the threshold of epidemic outbreak, the objective traveling can significantly enhance the final infected population and the infected fraction at a node is proportional to its betweenness for the traveling agents and approximately proportional to its degree for the non-traveling agents. Numerical simulations have confirmed the theoretical predictions.