[Paper Review] Unifying Markov Chain Approach for Disease and Rumor Spreading in Complex Networks

Guilherme Ferraz de Arruda, Francisco A. Rodrigues+3 more|arXiv (Cornell University)|Sep 2, 2016

Complex Network Analysis Techniques3 references4 citations

TL;DR

This paper proposes a unified discrete-time Markov chain framework that models both disease and rumor spreading in complex networks, incorporating mechanisms like apathy, forgetting, and interest recovery. It achieves high accuracy and computational efficiency by analytically deriving thresholds and dynamics, validated against Monte Carlo simulations and real-world Twitter data on the Higgs boson rumor.

ABSTRACT

Spreading processes are ubiquitous in natural and artificial systems. They can be studied via a plethora of models, depending on the specific details of the phenomena under study. Disease contagion and rumor spreading are among the most important of these processes due to their practical relevance. However, despite the similarities between them, current models address both spreading dynamics separately. In this paper, we propose a general information spreading model that is based on discrete time Markov chains. The model includes all the transitions that are plausible for both a disease contagion process and rumor propagation. We show that our model not only covers the traditional spreading schemes, but that it also contains some features relevant in social dynamics, such as apathy, forgetting, and lost/recovering of interest. The model is evaluated analytically to obtain the spreading thresholds and the early time dynamical behavior for the contact and reactive processes in several scenarios. Comparison with Monte Carlo simulations shows that the Markov chain formalism is highly accurate while it excels in computational efficiency. We round off our work by showing how the proposed framework can be applied to the study of spreading processes occurring on social networks.

Motivation & Objective

• Address the lack of a unified theoretical framework for modeling both disease and rumor spreading processes despite their phenomenological similarities.
• Integrate non-traditional mechanisms—such as apathy, forgetting, and lost/recovering interest—into a single dynamical model.
• Develop a computationally efficient alternative to Monte Carlo simulations for studying spreading dynamics on complex networks.
• Enable accurate prediction of temporal evolution and critical thresholds in both synthetic and real-world networks.
• Demonstrate applicability to real social network data, such as Twitter activity during the Higgs boson announcement.

Proposed method

• Formulate a discrete-time Markov chain model that captures all plausible state transitions for both epidemic and rumor spreading processes.
• Define state transitions including infection, recovery, spreading, stifling, apathy, forgetting, and interest recovery.
• Use mean-field approximations to derive analytical expressions for macroscopic properties like spreading thresholds and steady-state densities.
• Validate the model through extensive comparison with Monte Carlo simulations across different network types and scales.
• Apply the framework to real-world networks, including Twitter data, to reproduce empirical rumor propagation dynamics.
• Solve the system of differential equations numerically to predict time evolution and critical behavior under varying parameters.

Experimental results

Research questions

• RQ1 Can a single Markov chain framework unify the modeling of disease and rumor spreading while incorporating non-traditional behavioral mechanisms?
• RQ2 How do parameters such as apathy, forgetting, and interest recovery influence the spreading threshold and dynamics in complex networks?
• RQ3 To what extent does the Markov chain approach match Monte Carlo simulations in terms of accuracy and computational efficiency?
• RQ4 Can the model accurately reproduce real-world rumor propagation patterns, such as those observed during the Higgs boson announcement on Twitter?
• RQ5 What insights can be gained about the relative importance of different mechanisms in real contagion processes using this unified framework?

Key findings

• The proposed Markov chain model accurately reproduces the dynamics of both contact and reactive processes in complex networks, with results closely matching Monte Carlo simulations.
• The model successfully captures and generalizes traditional epidemic and rumor spreading models, including SIR, SIS, and the classic rumor spreading model with stiflers.
• Analytical expressions for the spreading threshold and steady-state densities were derived for the contact process and special cases of the reactive process.
• The framework enables the identification of dominant mechanisms in real contagion processes by fitting model parameters to empirical data, such as the Higgs boson rumor on Twitter.
• The computational cost of solving the Markov chain equations is significantly lower than Monte Carlo simulations, making it suitable for large-scale online social networks.
• The model reveals that mechanisms like forgetting and apathy play a crucial role in shaping the temporal evolution and final size of spreading processes in real networks.