Chaotic spreading of epidemics in complex networks of excitable units

Vannucchi, Fabio Stucchi; Boccaletti, Stefano

doi:10.3934/mbe.2004.1.49

Cited by 11 publications

(6 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The patchiness of the host distribution and of environmental conditions may contribute to the heterogeneous spread of epidemics in forests (e.g. Sander et al ., 2003; Vannucchi & Boccaletti, 2004). Models trying to include in their structure the variable susceptibility of hosts have certainly much scope for application in real forests (e.g.…”

Section: Potential Implications For Plant and Forest Pathologymentioning

confidence: 99%

Modelling disease spread and control in networks: implications for plant sciences

et al. 2007

View full text Add to dashboard Cite

SummaryNetworks are ubiquitous in natural, technological and social systems. They are of increasing relevance for improved understanding and control of infectious diseases of plants, animals and humans, given the interconnectedness of today's world. Recent modelling work on disease development in complex networks shows: the relative rapidity of pathogen spread in scale-free compared with random networks, unless there is high local clustering; the theoretical absence of an epidemic threshold in scale-free networks of infinite size, which implies that diseases with low infection rates can spread in them, but the emergence of a threshold when realistic features are added to networks (e.g. finite size, household structure or deactivation of links); and the influence on epidemic dynamics of asymmetrical interactions. Models suggest that control of pathogens spreading in scale-free networks should focus on highly connected individuals rather than on mass random immunization. A growing number of empirical applications of network theory in human medicine and animal disease ecology confirm the potential of the approach, and suggest that network thinking could also benefit plant epidemiology and forest pathology, particularly in human-modified pathosystems linked by commercial transport of plant and disease propagules. Potential consequences for the study and management of plant and tree diseases are discussed. Key words: complex networks, disease management, epiphytotics, landscape pathology, network structure, plant pathogens, small-world, spatial dispersal. IntroductionMuch scientific work is currently focusing on the properties of networks (see Barabási & Albert, 1999;Newman, 2003; papers cited therein). From a physical point of view, networks may involve transport of energy, matter or information. From a mathematical standpoint, networks are sets of elements and of the relations between them. From both perspectives, networks are models applicable to a wide variety of natural, technological and social systems (e.g. Strogatz, 2001; Albert & Barabási, 2002; Table 1). Networks can be of interest to plant scientists when they are formed by a physical structure, when they refer to abstract relationships between connected entities (e.g. different species), and when they underline processes or flows in a structure. Network types (SF, scale-free; SW, small-world; V, various types; N, none of the previous types) are assigned on the basis of the references provided and do not rule out the possibility that other studies of networks of a similar nature may suggest a different structure. For other references the reader is referred to reviews by, for example, Albert & Barabási (2002), Dorogovtsev & Mendes (2002) andNewman (2003). Network theory (e.g. Bollobás, 1979; Chartrand, 1985; Chen, 1997) has many practical biological applications in plant sciences, for example biochemical networks (Aloy & Russell, 2004; Arita, 2005; De Silva & Stumpf, 2005; Green & Sadedin, 2005;Proulx et al ., 2005;Sweetlove & Fernie, 2005;Uhrig, 20...

show abstract

Section: Potential Implications For Plant and Forest Pathologymentioning

confidence: 99%

Modelling disease spread and control in networks: implications for plant sciences

et al. 2007

View full text Add to dashboard Cite

show abstract

“…[371,372]. In particular, Vannucchi and Boccaletti have studied the dynamics of an epidemiological disease spreading on top of a complex network of individuals [371].…”

Section: Fluctuating Diseasesmentioning

confidence: 99%

“…The emergence of collective and synchronized dynamics in large networks of coupled units has been investigated since the beginning of the nineties in different contexts and in a variety of fields, ranging from biology and ecology [371,383,384], to semiconductor lasers [385][386][387][388], to electronic circuits [389,390].…”

Section: Synchronization and Collective Dynamicsmentioning

confidence: 99%

Complex networks: Structure and dynamics

et al. 2006

View full text Add to dashboard Cite

Coupled biological and chemical systems, neural networks, social interacting species, the Internet and the World Wide Web, are only a few examples of systems composed by a large number of highly interconnected dynamical units. The first approach to capture the global properties of such systems is to model them as graphs whose nodes represent the dynamical units, and whose links stand for the interactions between them. On the one hand, scientists have to cope with structural issues, such as characterizing the topology of a complex wiring architecture, revealing the unifying principles that are at the basis of real networks, and developing models to mimic the growth of a network and reproduce its structural properties. On the other hand, many relevant questions arise when studying complex networks' dynamics, such as learning how a large ensemble of dynamical systems that interact through a complex wiring topology can behave collectively. We review the major concepts and results recently achieved in the study of the structure and dynamics of complex networks, and summarize the relevant applications of these ideas in many different disciplines, ranging from nonlinear science to biology, from statistical mechanics to medicine and engineering.

show abstract

“…A regular lattice with the local dynamics of excitable elements is called excitable medium 1,2 . Sysa) Electronic mail: alexander@rothkegel.de b) Electronic mail: klaus.lehnertz@ukb.uni-bonn.de tems that have been modeled as excitable media are ubiquitous in nature, ranging from isothermal chemical reactions 3 via disease spreading among a population of living organisms 4 to the mammalian heart 5,6 and brain systems [7][8][9][10] . For many natural systems, however, the consideration of regular lattices may not yield an adequate description given that distant elements may interact.…”

Section: Introductionmentioning

confidence: 99%

Multistability, local pattern formation, and global collective firing in a small-world network of nonleaky integrate-and-fire neurons

Rothkegel

Lehnertz

2009

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

We investigate numerically the collective dynamical behavior of pulse-coupled nonleaky integrate-and-fire neurons that are arranged on a two-dimensional small-world network. To ensure ongoing activity, we impose a probability for spontaneous firing for each neuron. We study network dynamics evolving from different sets of initial conditions in dependence on coupling strength and rewiring probability. Besides a homogeneous equilibrium state for low coupling strength, we observe different local patterns including cyclic waves, spiral waves, and turbulentlike patterns, which-depending on network parameters-interfere with the global collective firing of the neurons. We attribute the various network dynamics to distinct regimes in the parameter space. For the same network parameters different network dynamics can be observed depending on the set of initial conditions only. Such a multistable behavior and the interplay between local pattern formation and global collective firing may be attributable to the spatiotemporal dynamics of biological networks.

show abstract

Chaotic spreading of epidemics in complex networks of excitable units

Cited by 11 publications

References 0 publications

Modelling disease spread and control in networks: implications for plant sciences

Modelling disease spread and control in networks: implications for plant sciences

Complex networks: Structure and dynamics

Multistability, local pattern formation, and global collective firing in a small-world network of nonleaky integrate-and-fire neurons

Contact Info

Product

Resources

About