Fast and exact simulations of stochastic epidemics on static and temporal networks

Epidemic models on complex networks have been widely used to study how the social structure of a population affect the spreading of epidemics. However, their numerical simulation can be computationally heavy, especially for large networks. In this paper, we introduce NEXT-Net: a flexible implementation of the next reaction method for epidemic spreading on both static and temporal networks. By systematic tests on artificial and real-world networks, we find that NEXT-Net is substantially faster than alternative algorithms, while being exact. It permits, in particular, to efficiently simulate epidemics on networks with million of nodes on a standard computer. It is also versatile enough to simulate a broad range of epidemic models of temporal networks, including cases in which the network structure changes in response to the epidemic. Our code is implemented in C++ and accessible from Python and R, thus combining speed with user friendliness. Because of these features, our algorithm constitutes an ideal tool for a broad range of applications.