Low Complexity Method for Simulation of Epidemics Based on Dijkstra's Algorithm

Zorzenon, Davide; Molinari, Fabio; Raisch, Joerg

Models of epidemics over networks have become popular, as they describe the impact of individual behavior on infection spread. However, they come with high computational complexity, which constitutes a problem in case large-scale scenarios are considered. This paper presents a discrete-time multi-agent SIR (Susceptible, Infected, Recovered) model that extends known results in literature. Based on that, using the novel notion of Contagion Graph, it proposes a graphbased method derived from Dijkstra's algorithm that allows to decrease the computational complexity of a simulation. The Contagion Graph can be also employed as an approximation scheme describing the"mean behavior"of an epidemic over a network and requiring low computational power. Theoretical findings are confirmed by randomized large-scale simulation.