Directed Dynamic Small-World Network Model for Worm Epidemics in Mobile ad hoc Networks

We investigate the worm spreading process in mobile ad hoc networks with a susceptible-infected-recovered model on a two-dimensional plane. A medium access control mechanism operates within it, inhibiting transmission and relaying a message by using other nodes inside the node's transmitting circle during speaking. We measure the rewiring probability p with the transmitting range r and the average relative velocity v of the moving nodes, and map the problem into a directed dynamic small-world network. A new scaling relation for the recovered portion of the nodes reveals the effect caused by geometric distance, which has been ignored by previous models.