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

TL;DR

This paper introduces a low-complexity, graph-based simulation method for epidemics using Dijkstra's algorithm, enabling efficient large-scale modeling of disease spread with theoretical and simulation validation.

Contribution

It proposes a novel contagion graph concept and a Dijkstra-based algorithm to reduce computational complexity in epidemic network simulations.

Findings

The method significantly decreases simulation time for large networks.

Contagion graph effectively approximates epidemic mean behavior.

Theoretical results are validated through large-scale randomized simulations.

Abstract

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.