Modeling Risk Perception in Networks with Community Structure

We study the influence of global, local and community-level risk perception on the extinction probability of a disease in several models of social networks. In particular, we study the infection progression as a susceptible-infected-susceptible (SIS) model on several modular networks, formed by a certain number of random and scale-free communities. We find that in the scale-free networks the progression is faster than in random ones with the same average connectivity degree. For what concerns the role of perception, we find that the knowledge of the infection level in one’s own neighborhood is the most effective property in stopping the spreading of a disease, but at the same time the more expensive one in terms of the quantity of required information, thus the cost/effectiveness optimum is a tradeoff between several parameters.

💡 Research Summary

This paper investigates how different levels of risk perception—global, local, and community—affect the extinction probability of an infectious disease modeled by the susceptible‑infected‑susceptible (SIS) process on modular networks. The authors construct two families of synthetic networks: (i) random (Erdős‑Rényi) communities and (ii) scale‑free (Barabási‑Albert) communities, each with the same average degree ⟨k⟩ and a configurable number of modules M. By keeping ⟨k⟩ constant, they isolate the impact of degree heterogeneity: scale‑free modules contain hubs that accelerate spread, leading to faster infection dynamics and lower extinction probabilities compared with random modules.

Risk perception is introduced as a dynamic modulation of the infection probability β. Three perception functions are defined: (1) Global perception, where every node adjusts β based on the instantaneous global prevalence I(t); (2) Local perception, where each node uses the fraction of infected neighbors i_loc to scale β; and (3) Community perception, where the average prevalence within a node’s own module i_comm is used. In each case the effective infection rate is β_eff = β·(1 − α·i), with α∈