How network properties and epidemic parameters influence stochastic SIR dynamics on scale-free random networks

ABSTRACT

With the premise that social interactions are described by power-law distributions, we study the stochastic dynamics of SIR (Susceptible-Infected-Removed) compartmental models on static scale-free random networks generated via the configuration model. We compare simulations of our model to analytical results, providing a closed formula and a lower bound for the probability of having a minor epidemic of the disease. We explore the variability in disease spread by stochastic simulations. In particular, we demonstrate how important epidemic indices change as a function of the contagiousness of the disease and the connectivity of the network. Our results quantify the role of the starting node’s degree in determining these indices, commonly used to describe epidemic spread. Our results and implementation set a baseline for studying epidemic spread on networks, showing how analytical methods can help in the interpretation of stochastic simulations.

KEYWORDS:

• Epidemic models
• configuration model
• scale-free networks
• spreaders in network
• Gillespie algorithm
• stochastic simulation

Acknowledgments

The authors thank Prof. Andrea Pugliese for his helpful comments and expert help in various stages of the manuscript. MS would like to thank the University of Trento for supporting his research during the final months of his PhD.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1. A positive solution ${\mathit{s}}^{\mathbf{\ast }}$ of $\mathit{s}=\mathit{f}(\mathit{s})$ is called the smallest if $s_i^{\ast }\le r_i$, for all $\mathit{i}=1,\dots ,\mathit{L}$, for any other solution $\mathit{r}$.

2. All the codes and additional data are available on https://github.com/SaraSottile/StochasticSIRnetwork.

Animations of sample simulations with different rates are available at

https://www.youtube.com/playlist?list=PLdDHYeVsbaLUY7-9gt9F01JEgIFm8D09m