Dynamical interplay between awareness and epidemic spreading in multiplex networks (1306.4136v2)

Abstract: We present the analysis of the interrelation between two processes accounting for the spreading of an epidemics, and the information awareness to prevent its infection, on top of multiplex networks. This scenario is representative of an epidemic process spreading on a network of persistent real contacts, and a cyclic information awareness process diffusing in the network of virtual social contacts between the same individuals. The topology corresponds to a multiplex network where two diffusive processes are interacting affecting each other. The analysis using a Microscopic Markov Chain Approach (MMCA) reveals the phase diagram of the incidence of the epidemics and allows to capture the evolution of the epidemic threshold depending on the topological structure of the multiplex and the interrelation with the awareness process. Interestingly, the critical point for the onset of the epidemics has a critical value (meta-critical point) defined by the awareness dynamics and the topology of the virtual network, from which the onset increases and the epidemics incidence decreases.

On the Dynamical Interplay Between Awareness and Epidemic Spreading in Multiplex Networks

The paper "On the dynamical interplay between awareness and epidemic spreading in multiplex networks" by Clara Granell, Sergio Gomez, and Alex Arenas presents an analytical and computational paper focusing on the interaction between epidemic spreading and information awareness within multiplex networks. The multiplex network model used in this paper is particularly significant as it captures the dual-layer structure of interactions: physical contact networks, where infection spreads, and virtual contact networks, where awareness of the infection propagates.

Methodology

The authors employ a Microscopic Markov Chain Approach (MMCA) to analyze the epidemic spreading (SIS model) and awareness diffusion (UAU model) on these interconnected networks. The multiplex network structure consists of a physical layer representing direct, real-world interactions among individuals and a virtual layer depicting online or indirect interactions. This novel setup allows for a nuanced analysis of how awareness influences epidemic thresholds and the prevalence of diseases.

Key Findings

1. Phase Diagram and Critical Thresholds: The MMCA method reveals the phase diagram of epidemic incidence and the critical points for the onset of the epidemic. The paper finds that the epidemic threshold is significantly influenced by the awareness dynamics and the topological structure of the virtual layer. Specifically, a meta-critical point arises, defined by the interaction of awareness and network topology, beyond which increased awareness leads to reduced epidemic incidence and delayed onset.
2. Numerical Accuracy: The MMCA predictions match Monte Carlo simulations with high accuracy, evidencing errors below 2.5%. This shows the MMCA’s robustness in capturing the dynamics of complex coupled processes within both homogeneous and heterogeneous network structures.
3. Epidemic Threshold Dependence on Awareness: As shown in the figures within the paper, the epidemic threshold $\beta_c$ is initially independent of the awareness spreading rate $\lambda$ but becomes increasingly dependent as $\lambda$ surpasses a certain critical value ($\lambda_c$). Beyond $\lambda_c$, awareness can effectively control and reduce the spread of the epidemic.

Implications

Practical Implications

• Public Health Strategies: The results have significant implications for designing public health interventions. Strategies enhancing awareness through social networks can effectively delay or even prevent the spread of infectious diseases by raising the disease threshold and reducing overall incidence.
• Social Network Utilization: Utilizing platforms like Facebook or Twitter for spreading awareness about diseases can be a potent tool in mitigating epidemic outbreaks, especially for diseases with well-understood transmission dynamics like the seasonal flu.

Theoretical Implications

• Multiplex Network Modeling: This research showcases the importance of considering multiplex networks when studying epidemic processes. Ignoring the multi-layered nature of interactions can lead to underestimating the influence of social behavior on disease dynamics.
• Dynamical Systems: The paper adds to the growing body of literature on coupled dynamical systems, particularly those involving antagonistic processes like infection and awareness. Understanding these interactions can pave the way for novel theoretical models in epidemiology and beyond.

Future Directions

Future research could expand on several aspects:

• Heterogeneous Awareness Dynamics: Incorporating more sophisticated models of awareness that include media influence and varying individual responses can provide a more detailed understanding.
• Multiple Layers and Dynamics: Expanding the analysis to include more than two layers or additional dynamic processes, such as vaccination behavior or governmental interventions, could help in formulating comprehensive public health policies.
• Empirical Validation: Applying these models to real-world data could help validate the theoretical predictions and refine the models for practical applications.

In summary, the paper provides valuable insights into the interplay between information awareness and epidemic spreading within multiplex networks. Its findings highlight the critical role that awareness can play in controlling epidemics, offering practical tools for public health and deepening our theoretical understanding of coupled dynamical systems.