Epidemics on Interconnected Networks (1201.6339v2)

Abstract: Populations are seldom completely isolated from their environment. Individuals in a particular geographic or social region may be considered a distinct network due to strong local ties, but will also interact with individuals in other networks. We study the susceptible-infected-recovered (SIR) process on interconnected network systems, and find two distinct regimes. In strongly-coupled network systems, epidemics occur simultaneously across the entire system at a critical infection strength $\beta_c$, below which the disease does not spread. In contrast, in weakly-coupled network systems, a mixed phase exists below $\beta_c$ of the coupled network system, where an epidemic occurs in one network but does not spread to the coupled network. We derive an expression for the network and disease parameters that allow this mixed phase and verify it numerically. Public health implications of communities comprising these two classes of network systems are also mentioned.

Analysis of Epidemics on Interconnected Networks

The paper "Epidemics on Interconnected Networks" by Dickison, Havlin, and Stanley presents an insightful examination of the propagation of infectious diseases across interconnected network systems using the susceptible-infected-recovered (SIR) model. Unlike traditional models that consider a single network, this research acknowledges the existence of numerous distinct yet interconnected networks, reflecting real-world social and geographical complexities. The paper systematically explores how the degree of coupling between networks affects epidemic spread, revealing complex dynamics that demand refined strategies for public health interventions.

The research categorizes interconnected networks into two regimes based on coupling strength: strongly coupled and weakly coupled. In strongly coupled networks, the spread of an epidemic is homogenous across all networks at or above a critical infection strength, $\beta_c$. The regime is characterized by $\kappa_T$, the expected number of nearest neighbors computed over the entire interconnected network, being greater than $\kappa_A$ and $\kappa_B$, which pertain to the individual networks. An epidemic in one network invariably leads to an outbreak in others, thereby requiring coordinated public health responses.

Conversely, weakly coupled networks, characterized by $\kappa_B > \kappa_T > \kappa_A$, manifest a mixed phase wherein an epidemic can occur in one network without significantly impacting others. This phase occurs when the infection strength is between $\beta_c(\kappa_B)$ and $\beta_c(\kappa_T)$. The paper derives conditions under which this mixed phase exists, showing that the spread is confined to the network with higher intranetwork connectivity, while others remain largely unaffected. Such findings are crucial for designing targeted interventions where resources can be concentrated within more vulnerable communities.

The paper makes use of extensive Monte Carlo simulations to validate the analytical results, effectively predicting the boundaries of different phases and illustrating the critical nature of coupling strength on epidemic thresholds. The survival probability $P(t)$, or the likelihood of an infection persisting over time, follows a power-law decay at criticality. The survival gap $\Delta P(t)$ between interconnected networks serves as an indicator of the presence of a mixed phase. This phase boundary and its properties exhibit scaling behavior indicative of universality, which can inform broader applications beyond the immediate epidemiological context described.

From a theoretical standpoint, this paper extends our understanding of network science by providing a comprehensive model for coupled epidemiological dynamics. The influence of internetwork links on epidemic transition phases underscores the importance of accounting for network structure heterogeneities in modeling infectious disease spread. Practically, the implications for public health policy are significant. Understanding the characteristics of network coupling can guide decisions on whether systemic intervention is required or if localized strategies suffices.

Future investigations should consider the scaling of this model to encompass more than two networks with heterogeneous sizes and structures, which could more accurately simulate real-world network dynamics. Additionally, incorporating temporal factors and adaptation of the network in response to disease spills would offer a richer canvas for understanding the emergent dynamics in complex adaptive systems. The incorporation of such complexities might be pivotal in developing adaptive, resilient strategies capable of mitigating epidemic risks in an interconnected world.