Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Sara Sottile, Ozan Kahramanoğulları, Mattia Sensi

Abstract

With the premise that social interactions are described by power-law distributions, we study a SIR stochastic dynamic on a static scale-free random network generated via configuration model. We verify our model with respect to deterministic considerations and provide a theoretical result on the probability of the extinction of the disease. Based on this calibration, 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 starting node degree in determining these indices, commonly used to describe epidemic spread.

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 a SIR stochastic dynamic on a static scale-free random network generated via configuration model. We verify our model with respect to deterministic considerations and provide a theoretical result on the probability of the extinction of the disease. Based on this calibration, 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 starting node degree in determining these indices, commonly used to describe epidemic spread.

Paper Structure

This paper contains 10 sections, 31 equations, 13 figures, 1 table.

Table of Contents

  1. Introduction
  2. Power-law networks
  3. Scale-free networks
  4. Configuration model
  5. Lower bound for the probability of extinction
  6. The stochastic model
  7. Deterministic vs. stochastic "hub case"
  8. Different numbers of initially infected nodes
  9. Initially infected nodes $I(0)=1$
  10. Discussion

Figures (13)

  • Figure 1: Plot of $R_0$ for the intervals of $\alpha$ and $\beta$ we are interested in.
  • Figure 2: Comparison between stochastic (red bars) and deterministic (blue bars) results.
  • Figure 3: Random choice of initially infected.
  • Figure 4: Mean-degree choice of initially infected.
  • Figure 5: Peripheral-degree choice of initially infected.
  • ...and 8 more figures

Theorems & Definitions (1)

  • Remark 1