Source-linked AI summary
Effects of awareness diffusion and self-initiated awareness behavior on epidemic spreading - an approach based on multiplex networks
Jia-Qian Kan, Hai-Feng Zhang
TL;DR
The paper asks how epidemic spreading and awareness diffusion interact when they occur on different layers of a multiplex network, including self-initiated awareness. Using a multiplex SIS-awareness model analyzed with Markov-chain methods and numerical computations, it finds that self-awareness reduces infection density but does not increase the epidemic threshold under local or global information.
Problem
The paper addresses how epidemic and awareness processes interact across separate multiplex-network layers when awareness can arise from informed neighbors, infected contacts, or mass media.
Method
The authors model SIS epidemic spreading on a contact layer and awareness diffusion on an information layer, then analyze the system with a Markov chain approach and numerical simulations.
Results
Self-awareness reduces infection density, but self-awareness behavior cannot alter the epidemic threshold under either local or global information.
Takeaways & Limitations
The results suggest that conclusions about awareness-based behavioral responses from single-layer networks may need re-examination in multiplex networks.
Takeaways & Limitations
The model assumes awareness changes infection risk through βA = γβ and treats γ = 0 as complete immunity for aware individuals.
Abstract
from arXiv · showhide
In this paper, we study the interplay between the epidemic spreading and the diffusion of awareness in multiplex networks. In the model, an infectious disease can spread in one network representing the paths of epidemic spreading (contact network), leading to the diffusion of awareness in the other network (information network), and then the diffusion of awareness will cause individuals to take social distances, which in turn affects the epidemic spreading. As for the diffusion of awareness, we assume that, on the one hand, individuals can be informed by other aware neighbors in information network, on the other hand, the susceptible individuals can be self-awareness induced by the infected neighbors in the contact networks (local information) or mass media (global information). Through Markov chain approach and numerical computations, we find that the density of infected individuals and the epidemic threshold can be affected by the structures of the two networks and the effective transmission rate of the awareness. However, we prove that though the introduction of the self-awareness can lower the density of infection, which cannot increase the epidemic threshold no matter of the local information or global information. Our finding is remarkably different to many previous results--local information based behavioral response can alter the epidemic threshold.
1 Introduction
The paper examines how epidemic spreading and awareness diffusion interact across multiplex networks. It focuses on combining awareness from information-network neighbors with self-initiated responses triggered by infected contacts or mass media.
- Motivation: Disease outbreaks can diffuse risk information that prompts protective behavior, affecting epidemic spread.Examples include reduced outings and mask wearing during H1N1, bird flu, and SARS outbreaks.
- Research gap: Earlier studies often placed epidemic and information spreading in the same network, whereas multiplex networks represent their different channels.Information may spread through word of mouth, news media, or online social networks.
- Research gap: The paper combines self-initiated awareness with awareness transmitted by informed neighbors, addressing a combination that previous work had not well studied.The model includes self-awareness induced by infected neighbors in the contact network or by mass media.
- Approach: The study uses a multiplex-network model, Markov-chain analysis, simulations, and theoretical analysis to investigate epidemic-awareness interplay.The paper introduces the model, presents simulation and theoretical results, and discusses conclusions; global-information results appear in an appendix.
2 Model
The model places SIS epidemic dynamics on a contact layer and awareness diffusion on an information layer sharing the same individuals. Awareness changes infection risk and can arise through infected individuals, aware neighbors, infected contacts, or mass media.
- Network structure: The multiplex has a contact layer for epidemic spreading and an information layer for awareness diffusion, with identical individuals but different connectivity.The contact layer uses a susceptible-infected-susceptible framework.
- State transitions: Infected individuals become aware with probability σ, while unaware and aware susceptible nodes face infection probabilities β and βA = γβ, respectively.When γ = 0, aware individuals are completely immune to infection.
- Self-awareness: A susceptible individual can become aware with probability κ after contacting an infected friend, making self-awareness depend on infected neighbors in the contact network.The probability of awareness increases with the number of infected neighbors.
- State space: The model represents each individual in one of four states: susceptible-unaware, susceptible-aware, infected-unaware, or infected-aware.The state transitions are summarized in the paper's flow diagram.
3 Main results
The model combines SIS epidemic spreading on a contact network with UAU awareness diffusion on an information network, including awareness induced locally or globally. Markov-chain analysis and simulations show that self-awareness lowers infection density but does not change the epidemic threshold.
- Model and analysis: The multiplex model assigns individuals four states—SU, SA, IU, and IA—by combining infection status with awareness status.Epidemic transmission occurs on the contact layer, while awareness spreads on the information layer.
- Model and analysis: MMCA equations are derived from transition-probability trees for the four UAU-SIS states, and the epidemic threshold follows from the largest eigenvalue of matrix H.Near threshold, infected-node probabilities are treated as tending to zero.
- Numerical validation: MMCA results agree well with Monte Carlo simulations under the tested parameter settings.Subsequent numerical results therefore use MMCA as the main computational approach.
- Effects of self-awareness: Larger κ increases awareness and reduces infection density, especially at larger β, but does not alter the epidemic threshold.Near or below threshold, κ changes the initial number of aware individuals without changing stationary awareness density.
- Effects of self-awareness: Varying σ has negligible effects on infection density and does not change the epidemic threshold, including the extreme cases σ = 0 and σ = 1.The corresponding awareness and infection densities are examined as functions of β.
- Overall results: Across the phase diagram, infection density decreases with λ and κ above the epidemic threshold, while it is unaffected by λ below threshold because the epidemic dies out.The analysis concludes that self-awareness cannot alter the threshold for either local or global information.
4 Conclusions and discussions
The multiplex model incorporates self-awareness triggered by infected neighbors or other information channels and examines its effects on epidemic spreading. Self-awareness lowers infection density, but does not alter the epidemic threshold, contrasting with single-layer results.
- The model studies self-awareness of susceptible and infected individuals within separate contact and information layers of a multiplex network.The parameters κ and σ characterize self-awareness probabilities for susceptible and infected individuals, respectively.
- Increasing κ and σ reduces infection density, with susceptible individuals’ self-awareness providing stronger inhibition than infected individuals’ self-awareness.Susceptible self-awareness directly lowers individuals’ infection probabilities.
- Self-awareness does not alter the epidemic threshold under either local or global information.This result contrasts with findings from single-layer networks.
- The conclusions obtained for awareness-driven behavioral responses in single-layer networks may need re-examination when extended to multiplex networks.
6 Apendix: Global information-based awareness
The appendix models global information-based awareness as adaptive mass-media awareness tied to infection density. Its analysis finds that changing the mass-media parameter does not affect the epidemic threshold, across different infected-awareness responses.
- Global information-based awareness occurs with probability mI(t), so awareness adapts to the current density of infection.This replaces a fixed mass-media awareness probability with an infection-dependent one.
- The global-information case is obtained by changing γ_i(t) and θ_i(t) in the local model.
- The epidemic threshold remains independent of m, differing from the result reported in Ref..The result is verified for different values of γ.
- Figure 7 plots infected density against β for different m values while varying γ across four panels.The other parameters are fixed at λ = 0.3, σ = 0.5, δ = 0.6, µ = 0.4, and κ = 0.0.