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

Epidemic models on complex networks are widely used to assess how the social structure of a population affects epidemic spreading. 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 simulating epidemic spreading on both static and temporal weighted 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 millions of nodes on a standard computer. It also permits simulating a broad range of epidemic models on temporal networks, including scenarios in which the network structure changes in response to the epidemic. NEXT-Net is implemented in C++ and accessible from Python and R, thus combining speed with user friendliness. These features make our algorithm an ideal tool for a broad range of applications.Author summary: Human social structures tend to be quite heterogeneous, with some individuals having many more social interactions than others. These social structures profoundly affect the spreading of epidemics and can be conveniently conceptualized as networks, in which nodes represent individuals and links represent contacts. However, computer simulations of epidemic models on networks can be slow, and efficient numerical methods are understudied. This prevents computer simulations of epidemics on realistically large networks. In this paper, we present NEXT-Net: an algorithm to efficiently simulate epidemic spreading on networks. Our algorithm can simulate a broad class of models, including networks whose structure evolves in time. Its versatility, ease of use, and performance make it broadly useful for epidemiological studies.