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

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