[Paper Review] On the propagation of social epidemics in social networks under S.I.R. model

Horacio Castellini, Lilia Romanelli|ArXiv.org|Mar 26, 2007

Complex Network Analysis Techniques7 references3 citations

TL;DR

This study extends the S.I.R. model to social epidemics in complex networks by simulating information propagation in scale-free (SF), small-world (SM), and empirically derived networks (LM, DM). It introduces a threshold-based interaction model with stochastic infection probabilities, revealing that real-world networks (LM, DM) yield significantly higher survival rates than theoretical models (SF, SM), challenging the reliability of synthetic network simulations for epidemic spread prediction.

ABSTRACT

The S.I.R. model (Susceptible, Infected, Recovered or Died) was proposed by chemistry Willam Kermack (1927) and the mathematician G. Mc. Kendrick (1932). the model supposes to divide to the individuals of a population in three categories. Susceptible to be infected, Infected and Recovered (immune or died by the disease). On the other hand has been a similarity in the evolution of epidemics of infect aerial, the computer science propagation of virus and the propagation of social paradigms (fashion, rumor, etc.) it calls modernly ``Social Epidemics''. In this work it is tried to use this model in different types from social networks, real or not. In order to evaluate a meta-analysis of results allows to investigate under wich conditions the topology of the network is excellent and that networks are equivalent. The result obtained can have relevance in study of propagation of epidemics of different types.

Motivation & Objective

• To assess how network topology influences the propagation of social epidemics using a modified S.I.R. model.
• To compare survival probabilities and structural stability between real-world social networks (LM, DM) and synthetic models (SF, SM).
• To determine whether theoretical network models accurately simulate real social epidemic dynamics.
• To evaluate the reliability of synthetic networks in predicting epidemic outcomes under threshold-based interaction rules.

Proposed method

• A custom epidemic algorithm models information spread using adjacency matrices (AM) derived from real or synthetic networks.
• Each actor is assigned a susceptibility threshold (U), a 32-bit state vector, and a health state (S, E, M), with state transitions based on Hamming distance and threshold conditions.
• Infection probability between connected actors is modeled as a uniform random variable C ∈ [0,1], simulating variable transmission likelihood.
• Interactions occur only when the Hamming distance between two actors' state vectors is below the minimum of their thresholds.
• Survival probability and variance of final network structures are computed across multiple simulation runs for different threshold values (U = 10 to 20).
• Meta-analysis is performed using difference of proportions (DR) and 95% confidence intervals to test equivalence between network types.

Experimental results

Research questions

• RQ1 How does network topology (scale-free vs. small-world vs. real-world) affect the survival probability of individuals in a social epidemic?
• RQ2 Are synthetic network models (SF, SM) equivalent to real-world networks (LM, DM) in terms of epidemic outcome distribution?
• RQ3 Does the threshold-based interaction rule lead to significantly different survival dynamics compared to purely random mixing?
• RQ4 What is the statistical significance of differences in survival rates between real and synthetic networks?
• RQ5 Can theoretical network models reliably simulate real social epidemic propagation under the same epidemic rules?

Key findings

• For U = 15, survival probability exceeds 50% in LM and DM networks (P(S) = 0.30 and 0.41), while SF and SM networks show lower survival (P(S) = 0.60 and 0.58).
• Variance in survival outcomes peaks at U = 15 (V(S) = 1769.68 for SF, 3704.39 for LM), indicating high structural diversity in final network states.
• Meta-analysis shows LM and DM networks are statistically equivalent (DR = 0.02 ± 0.09), with 95% confidence interval including zero.
• LM vs. SM comparison yields DR = 0.28 ± 0.06, rejecting the null hypothesis and indicating significant differences in survival rates.
• SF vs. SM comparison yields DR = 0.02 ± 0.021, marginally supporting equivalence but with limited statistical confidence.
• The study concludes that real-world networks (LM, DM) are not equivalent to theoretical models (SF, SM), undermining the reliability of synthetic networks in simulating social epidemic spread.