Reply to “Comment on ‘Linking population-level models with growing networks: A class of epidemic models’ ”

We disagree with Bootsma and Diekmann that our formula for the basic reproduction ratio $\left(R_0\right)$ has an underlying conceptual mistake. In Phys. Rev. E 72, 046110 (2005), we propose a large class of growing networks (which we call Kinetic Monte Carlo (KMC) growing networks) as individual-level models for the transmission of infectious diseases. KMC growing networks are conceptually different from the well-established Crump-Mode-Jagers continuous-time branching processes. Thus, the branching process definition of $R_0$ is not valid for KMC growing networks, and a different implementation of the biological definition of $R_0$ is necessary.