Epidemic Dynamics on an Adaptive Network

Abstract

Many real-world networks are characterized by adaptive changes in their topology depending on the state of their nodes. Here we study epidemic dynamics on an adaptive network, where the susceptibles are able to avoid contact with the infected by rewiring their network connections. This gives rise to assortative degree correlation, oscillations, hysteresis, and first order transitions. We propose a low-dimensional model to describe the system and present a full local bifurcation analysis. Our results indicate that the interplay between dynamics and topology can have important consequences for the spreading of infectious diseases and related applications. DOI: 10.1103/PhysRevLett.96.208701 PACS numbers: 89.75.Hc, 87.19.Xx, 89.75.Fb In the physical literature the dynamics of complex networks has recently received much attention, with many applications in social, biological, and technical systems [1,2]. In particular, most research has been directed in two distinct directions. On the one hand, attention has been paid to the structure of the networks, revealing that simple dynamical rules, such as preferential attachment or selective rewiring, can be used to generate complex topologies [3][4][5][6]. Many of these rules are not only a useful tool for the generation of model graphs, but are also believed to shape real-world networks like the internet or the network of social contacts. On the other hand, research has focused on large ensembles of dynamical systems, where the interaction between individual units is described by a complex graph [7][8][9][10][11][12][13][14][15]. These studies have shown that the network topology can have a strong impact on the dynamics of the nodes, e.g., the absence of epidemic thresholds on scale free networks [7,8] or the detrimental effect of assortative degree correlations on targeted vaccination [12]. In the past the cross fertilization between these two lines of thought has led to considerable advances. However, the dynamics of networks and the dynamics on networks are still generally studied separately. In doing so, a characteristic features of many real-world networks is not taken into account, namely, the ability to adapt the network topology dynamically in response to the dynamic state of nodes [16 -19].Consider, for example, the spreading of an infectious disease on a social network. Humans tend to respond to the emergence of an epidemic by avoiding contacts with infected individuals. Such rewiring of the local connections can have a strong effect on the dynamics of the disease, which in turn influences the rewiring process. Thus, a complicated mutual interaction between a time varying network topology and the dynamics of the nodes emerges.In this Letter we study a susceptible-infectedsusceptible (SIS) model on an adaptive network. We demonstrate that a simple intuitive rewiring rule for the network connections has a profound impact on the emerging network, and is able to generate specific network properties such as a wide degree distribution, assortative degree correlatio...

Contact switching as a control strategy for epidemic outbreaks

“…Recently, it has been suggested that a different kind of strategy, implemented by the individuals themselves, could give surprisingly positive results in controlling disease spreading (Gross et al, 2006;Zanette and Risau-Gusman, 2008). The basic idea is that contact between non-infective and infective acquaintances must be systematically avoided.…”

“…If the social connectivity is nevertheless to be preserved, those broken links must be replaced by new connections. In the SIS (susceptible → infective → susceptible) epidemiological model analyzed by Gross et al (2006), it is susceptible agents who break contacts with their infective neighbors, what necessarily leads to the isolation of infective agents, and new connections are established only with other susceptible agents. Implicitly, this assumes that the epidemiological state of all agents is known to any other agent, irrespectively of whether they are connected or not.…”

Causality-driven slow-down and speed-up of diffusion in non-Markovian temporal networks

“…Other works show that the dynamics of network topologies can introduce noise that fosters certain types of consensus processes 2,3 . Assuming that network topologies change in response to the dynamical process running on top of it, another line of research has studied adaptive networks, again highlighting that network dynamics have important consequences for dynamical processes 6,7 . Considering interactions in dynamic networks as a time series of events, a number of recent works focused on the question of whether observed inter-event times are consistent with the Poissonian distribution expected from a memoryless stochastic process.…”

Analytic description of adaptive network topologies in a steady state

“…Analytic expressions for the ensuing degree distributions have been so far lacking, and their investigation has relied on numerical procedures [4][5][6][7]. As a consequence, the distributions' dependency on system parameters is difficult to infer and small parameter regions with counterintuitive topologies prone to be overlooked.Here, we revisit the adaptive contact process in dynamic equilibrium [11]. Using a compartmental approach [12], we obtain closed-form ensemble degree distributions dependent on a single external parameter, and show that a coarse-grained understanding of the distributions' shapes can be obtained self-containedly.…”

“…In particular, the emergence of symmetric ensemble statistics from asymmetric dynamics can be explained. The framework's applicability to static networks as well as to other coevolutionary dynamics is also discussed.Model.-The contact process on an adaptive network models the spreading of a disease in a population without immunity, but with disease awareness [11]. The disease is transmitted along active links that connect infected I-nodes with susceptible S-nodes, letting the susceptible end switch to the Istate with rate p. Moreover, I-nodes recover to the S-state with rate r. Additionally, S-nodes evade infection by retracting active links with rate w and rewiring them to randomly selected S-nodes.…”