Competing spreading processes on multiplex networks: awareness and epidemics (1405.4480v1)

Abstract: Epidemic-like spreading processes on top of multilayered interconnected complex networks reveal a rich phase diagram of intertwined competition effects. A recent study by the authors [Granell et al. Phys. Rev. Lett. 111, 128701 (2013)] presented the analysis of the interrelation between two processes accounting for the spreading of an epidemics, and the spreading of information awareness to prevent its infection, on top of multiplex networks. The results in the case in which awareness implies total immunization to the disease, revealed the existence of a metacritical point at which the critical onset of the epidemics starts depending on the reaching of the awareness process. Here we present a full analysis of these critical properties in the more general scenario where the awareness spreading does not imply total immunization, and where infection does not imply immediate awareness of it. We find the critical relation between both competing processes for a wide spectrum of parameters representing the interaction between them. We also analyze the consequences of a massive broadcast of awareness (mass media) on the final outcome of the epidemic incidence. Importantly enough, the mass media makes the metacritical point to disappear. The results reveal that the main finding i.e. existence of a metacritical point, is rooted on the competition principle and holds for a large set of scenarios.

Analysis of Competing Spreading Processes on Multiplex Networks: Awareness and Epidemics

The interplay between disease spread and information dissemination processes over multiplex networks presents unique challenges and insights into epidemic modeling. The paper by Clara Granell, Sergio Gómez, and Alex Arenas addresses this intersection by examining how an awareness layer, which may confer partial immunity to nodes, interacts with the epidemic spreading process.

Summary of Key Findings

1. Model Framework: This research extends the understanding of epidemic dynamics by considering a two-layer multiplex network model. The layers represent physical human interactions (epidemic layer) and information sharing (awareness layer). The model is based on Susceptible-Infected-Susceptible (SIS) and Unaware-Aware-Unaware (UAU) processes, with parameters such as the disease infectivity rate ($\beta$), the rate of becoming aware ($\lambda$), and recovery/immunity from awareness ($\gamma$).
2. Impact of Awareness: The critical findings demonstrate that the presence of an awareness layer can mitigate the spread of an epidemic. Specifically, the interaction between the layers through awareness that does not necessarily lead to complete immunity shows nuanced effects on the epidemic threshold. The degree of immunization ($\gamma$) significantly affects the critical properties, altering the epidemic threshold $\beta_c$.
3. Mass Media Effect: The inclusion of mass media, modeled as a global awareness source, significantly affects the epidemic's dynamics by eliminating the metacritical point. The mass media presence essentially ensures that a certain fraction of the population remains aware regardless of the epidemic spread, thus impacting the onset and control of the epidemic.
4. Microscopic Markov Chain Approach (MMCA): The paper employs this analytic approach to derive the probabilities of nodes transitioning between states, offering a rigorously methodological way to simulate dynamics and derive thresholds, aiding in understanding the complex interdependencies of the network layers.
5. Parameter Sensitivity: The paper highlights the influence of key parameters:
   • Immunization ($\gamma$): Variations significantly alter epidemic onset, with lower $\gamma$ (higher immunity effect) shifting thresholds upward.
   • Self-awareness ($\kappa$): Surprisingly, variations in self-awareness have negligible effects on epidemic onset or dynamics.
   • Mass media ($m$): Larger $m$ values substantially shift epidemic thresholds, indicating strong control over epidemic spread when mass media is active.

Implications and Future Research Directions

These results underscore the complex nature of multiplex networks, where multiple layers can non-trivially affect epidemic outcomes. Practically, this paper suggests that leveraging mass media effectively could be a potent strategy for epidemic control without relying solely on individual immunity or self-awareness strategies.

Theoretically, this work opens avenues for exploring various combinations of awareness and epidemic models beyond the binary immunization paradigm. There is potential for future research to examine other types of information processes or networks with varying structures or time-varying connectivity.

Conclusion

Granell et al. have delivered a comprehensive exploration of competing processes in multiplex networks, adding valuable knowledge to the field of network epidemiology. The insights provided by their model and analyses could improve strategic public health interventions and inform better frameworks for predicting disease spread in the presence of complex human interactions and information dissemination processes.