The alternative approach to simulating disease processes on networks is to simulate a series of stochastic Markovian events-the continuous-time approach. Essentially, given the state of the system, it is possible to calculate the probability distributions of when possible subsequent events (i.e., recovery of an infectious node or infection of a susceptible node) will occur. Random draws from these distributions are then made to determine which event occurs next, the state of the system updated, and the process repeated. This approach was pioneered by Gillespie to study the dynamics of chemical reactions [110] ; it is, however, computationally intensive, so approximations have been developed. The τleap method [111] , where multiple events are allowed to occur during a time period τ, is clearly related to the discretetime formulation discussed above. However, the ability to allow τ to vary during a simulation to account for the processes involved [112] has potential benefits.