Networked SIS Epidemics With Awareness

Abstract

We study an SIS epidemic process over a static contact network where the nodes have partial information about the epidemic state. They react by limiting their interactions with their neighbors when they believe the epidemic is currently prevalent. A node's awareness is weighted by the fraction of infected neighbors in their social network, and a global broadcast of the fraction of infected nodes in the entire network. The dynamics of the benchmark (no awareness) and awareness models are described by discrete-time Markov chains, from which mean-field approximations (MFA) are derived. The states of the MFA are interpreted as the nodes' probabilities of being infected. We show a sufficient condition for existence of a "metastable", or endemic, state of the awareness model coincides with that of the benchmark model. Furthermore, we use a coupling technique to give a full stochastic comparison analysis between the two chains, which serves as a probabilistic analogue to the MFA analysis. In particular, we show that adding awareness reduces the expectation of any epidemic metric on the space of sample paths, e.g. eradication time or total infections. We characterize the reduction in expectations in terms of the coupling distribution. In simulations, we evaluate the effect social distancing has on contact networks from different random graph families (geometric, Erdős-Renyi, and scale-free random networks).

Game-Theoretic Vaccination Against Networked SIS Epidemics and Impacts of Human Decision-Making

“…We further characterize the socially optimal vaccination policy and investigate the inefficiency of Nash equilibrium. tions of steady-state behavior [13,14], centralized protection strategies to control the spreading processes [15,4], and network designs that are resilient against the epidemic [16,17]; see [18,2] for recent reviews. While centralized protection strategies are not practical for large-scale networked systems, decentralized and game-theoretic protection strategies against network epidemics have been relatively less explored [18,2].…”

Reacting to outbreaks at neighboring localities

“…Reduction in both metrics reaches above 60% when α i = 5. While both metrics continue to decrease with α i increasing, there does not exist a critical threshold of α i that stops the outbreak from happening [15][16][17]. We observe a slight decrease in time of peak from day 37 to day 35 as α i increases from 0 to 5.…”

“…Our focus is on the role of behavior changes in different localities and the effects of behavior changes on local disease progression. We assume individuals change their behavior and reduce their contacts proportional to disease severity, i.e., the ratio of infected and recovered, in the population [15,16]. In addition, behavior in a locality can be affected by the disease severity in neighboring localities.…”

Information Diffusion in Social Networks: Friendship Paradox Based Models and Statistical Inference

“…Modeling a network as a deterministic graph does not capture information diffusion processes in real world networks. Several works proposed and analyzed evolving graph models: [72] studied the adaptive susceptible-infected-susceptible (ASIS) model where susceptible individuals are allowed to temporarily cut edges connecting them to infected nodes in order to prevent the spread of the infection, [75] analyzed the stability of epidemic processes over time-varying networks and provides sufficient conditions for convergence, [73] studied a SIS process over a static contact network where the nodes have partial information about the epidemic state and react by limiting their interactions with their neighbors when they believe the epidemic is 1 The concept of monophily presented in [2] does not give a causal interpretation but only the correlation between two-hop neighbors of an undirected graph. What we consider is monophilic contagion (motivated by monophily): the information diffusion caused by the influence of two hop neighbors in an undirected network.…”