Multi-state epidemic processes on complex networks

Masuda, Naoki; Konno, Norio

doi:10.1016/j.jtbi.2006.06.010

Cited by 85 publications

(57 citation statements)

References 51 publications

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“…As we already pointed out, models for epidemic spreading are closely related to the metacommunity model discussed here. For example, in ongoing investigations on simultaneous spreading of several (competing) diseases [164][165][166][167] our results can be viewed from a different perspective: While in ecology the maintenance of species diversity is desirable, in epidemiology one aims to contain the diversity of diseases. Therefore, the proposed approach can be used to determine those parameter ranges where certain diseases go extinct, and to develop means for driving the system into the desired regime.…”

Section: Discussionmentioning

confidence: 99%

Emergence and persistence of diversity in complex networks

Böhme

2013

Eur. Phys. J. Spec. Top.

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Complex networks are employed as a mathematical description of complex systems in many different fields, ranging from biology to sociology, economy and ecology. Dynamical processes in these systems often display phase transitions, where the dynamics of the system changes qualitatively. In combination with these phase transitions certain components of the system might irretrievably go extinct. In this case, we talk about absorbing transitions. Developing mathematical tools, which allow for an analysis and prediction of the observed phase transitions is crucial for the investigation of complex networks.In this thesis, we investigate absorbing transitions in dynamical networks, where a certain amount of diversity is lost. In some real-world examples, e.g. in the evolution of human societies or of ecological systems, it is desirable to maintain a high degree of diversity, whereas in others, e.g. in epidemic spreading, the diversity of diseases is worthwhile to confine. An understanding of the underlying mechanisms for emergence and persistence of diversity in complex systems is therefore essential. Within the scope of two different network models, we develop an analytical approach, which can be used to estimate the prerequisites for diversity.In the first part, we study a model for opinion formation in human societies. In this model, regimes of low diversity and regimes of high diversity are separated by a fragmentation transition, where the network breaks into disconnected components, corresponding to different opinions. We propose an approach for the estimation of the fragmentation point. The approach is based on a linear stability analysis of the fragmented state close to the phase transition and yields much more accurate results compared to conventional methods.In the second part, we study a model for the formation of complex food webs. We calculate and analyze coexistence conditions for several types of species in ecological communities. To this aim, we employ an approach which involves an iterative stability analysis of the equilibrium with respect to the arrival of a new species. The proposed formalism allows for a direct calculation of coexistence ranges and thus facilitates a systematic analysis of persistence conditions for food webs.In summary, we present a general mathematical framework for the calculation of absorbing phase transitions in complex networks, which is based on concepts from percolation theory. While the specific implementation of the formalism differs from model to model, the basic principle remains applicable to a wide range of different models.

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Section: Discussionmentioning

confidence: 99%

Emergence and persistence of diversity in complex networks

Böhme

2013

Eur. Phys. J. Spec. Top.

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“…edge weights [22,21], temporal variance [23], and epidemic dynamics [24,25]. At the other extreme and similar in spirit to our work is EpiSims [26], which uses detailed infrastructure and traffic data of a single city and simulates on the scale of seconds; however it does not extend easily to other and larger populations.…”

Section: Introductionmentioning

confidence: 94%

Simulating Individual-Based Models of Epidemics in Hierarchical Networks

Quax

Bader

Sloot

2009

Lecture Notes in Computer Science

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Abstract. Current mathematical modeling methods for the spreading of infectious diseases are too simplified and do not scale well. We present the Simulator of Epidemic Evolution in Complex Networks (SEECN), an efficient simulator of detailed individual-based models by parameterizing separate dynamics operators, which are iteratively applied to the contact network. We reduce the network generator's computational complexity, improve cache efficiency and parallelize the simulator. To evaluate its running time we experiment with an HIV epidemic model that incorporates up to one million homosexual men in a scale-free network, including hierarchical community structure, social dynamics and multi-stage intranode progression. We find that the running times are feasible, on the order of minutes, and argue that SEECN can be used to study realistic epidemics and its properties experimentally, in contrast to defining and solving ever more complicated mathematical models as is the current practice.

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“…Indeed, many results for these models are derived in the large-population limit, at Next-generation operator [9][10][11][12] Local stability of disease-free equilibrium [13][14][15][16][17][18][19][20] Existence of an endemic equilibrium [21][22][23] Multiple criteria [24][25][26][27] which point the stochastic behavior is well-approximated by a corresponding deterministic model (for a more precise statement, see the work of Kurtz [6,7] and Jacquez and Simon [8]). For the remainder of this article, we will explicitly focus on deterministic models, but the results of Sections 4 and 5 are useful in both deterministic and stochastic settings.…”

Section: Thresholds In Disease Modelsmentioning

confidence: 99%

“…This approach has been taken by a number of researchers; some recent examples include [10,13,14,35] and [23]. We make the assumption of identical biology, as described in Section 2.…”

Section: A Structured Populationmentioning

confidence: 99%

Epidemic thresholds for infections in uncertain networks

Zager

Verghese

2008

Complexity

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Over the last 10 years, the field of mathematical epidemiology has piqued the interest of complex-systems researchers, resulting in a tremendous Periodicals, Inc. Complexity 14: 12-25, 2009 Key Words: epidemic; network; basic reproductive ratio; local asymptotic stability; spectral radius approximation; spectral graph theory; uncertain network THRESHOLDS IN DISEASE MODELSA major objective of mathematical epidemiology is to serve public health interests by modeling the essential characteristics of disease transmission. Until the acceptance of the germ theory of infection in the late nineteenth century, disease modeling was limited to a posteriori statistical analysis of outbreaks. Once the biological mechanisms of infection propagation were understood, dynamic modeling became the approach of choice. The central modeling paradigm of mathematical epidemiology is the compartmental model, which tracks individuals as they transition between different disease compartments, classified by the compartment's ability to acquire and transmit infection. The general model will be described in Section 2, but an orienting example is shown in Figure 1, which depicts a simple model for a susceptibleinfected-susceptible (SIS) infection transmitted between two subpopulations. The Researchers are often interested in using disease models to determine whether or not a disease will become an "epidemic." In public health, this term is often loosely defined as "any marked upward fluctuation in disease incidence or prevalence" [1]. Often, researchers refer to a disease progression as an epidemic if a small initial infective population can grow in size, whereas others associate an epidemic with the establishment of an endemic presence, i.e., a sustained positive level of infection. This article was submitted as an invited paper resulting from the "UnderstandingIn stochastic models, one is often interested in the time scales over which the disease is likely to be present. For example, Ganesh et al. identify sufficient conditions for the expected time to extinction of an SIS infection to be of order log(n) (fast die-out, no epidemic) on a network of n nodes, or of order exp(n α ), α > 0 (slow die-out, or effectively endemic) [2]. For additional interpretations of "epidemic" in stochastic models, see the work of Nasell [3], Newman [4], and Miller [5].Although the spread of infection is ideally modeled stochastically, as an individual-to-individual phenomenon, stochastic models can quickly become analytically intractable. Indeed, many results for these models are derived in the large-population limit, at Local stability of disease-free equilibrium [13][14][15][16][17][18][19][20] Existence of an endemic equilibrium [21][22][23] Multiple criteria [24][25][26][27] which point the stochastic behavior is well-approximated by a corresponding deterministic model (for a more precise statement, see the work of Kurtz [6,7] and Jacquez and Simon [8]). For the remainder of this article, we will explicitly focus on deterministic models, but the results ...

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Multi-state epidemic processes on complex networks

Cited by 85 publications

References 51 publications

Emergence and persistence of diversity in complex networks

Emergence and persistence of diversity in complex networks

Simulating Individual-Based Models of Epidemics in Hierarchical Networks

Epidemic thresholds for infections in uncertain networks

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