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Register a new userEffect of Coupling on the Epidemic Threshold in Interconnected Complex Networks: A Spectral Analysis
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In epidemic modeling, the term infection strength indicates the ratio of infection rate and cure rate. If the infection strength is higher than a certain threshold -- which we define as the epidemic threshold - then the epidemic spreads through the population and persists in the long run. For a single generic graph representing the contact network of the population under consideration, the epidemic threshold turns out to be equal to the inverse of the spectral radius of the contact graph. However, in a real world scenario it is not possible to isolate a population completely: there is always some interconnection with another network, which partially overlaps with the contact network. Results for epidemic threshold in interconnected networks are limited to homogeneous mixing populations and degree distribution arguments. In this paper, we adopt a spectral approach. We show how the epidemic threshold in a given network changes as a result of being coupled with another network with fixed infection strength. In our model, the contact network and the interconnections are generic. Using bifurcation theory and algebraic graph theory, we rigorously derive the epidemic threshold in interconnected networks. These results have implications for the broad field of epidemic modeling and control. Our analytical results are supported by numerical simulations.
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Interconnected networks are mathematical representation of systems where two or more simple networks are coupled to each other. Depending on the coupling weight between the two components, the interconnected network can function in two regimes: one where the two networks are structurally distinguishable, and one where they are not. The coupling threshold--denoting this structural transition--is one of the most crucial concepts in interconnected networks. Yet, current information about the coupling threshold is limited. This letter presents an analytical expression for the exact value of the coupling threshold and outlines network interrelation implications.
This study is concerned with the dynamical behaviors of epidemic spreading over a two-layered interconnected network. Three models in different levels are proposed to describe cooperative spreading processes over the interconnected network, wherein the disease in one network can spread to the other. Theoretical analysis is provided for each model to reveal that the global epidemic threshold in the interconnected network is not larger than the epidemic thresholds for the two isolated layered networks. In particular, in an interconnected homogenous network, detailed theoretical analysis is presented, which allows quick and accurate calculations of the global epidemic threshold. Moreover, in an interconnected heterogeneous network with inter-layer correlation between node degrees, it is found that the inter-layer correlation coefficient has little impact on the epidemic threshold, but has significant impact on the total prevalence. Simulations further verify the analytical results, showing that cooperative epidemic processes promote the spreading of diseases.
In the real world, many complex systems interact with other systems. In addition, the intra- or inter-systems for the spread of information about infectious diseases and the transmission of infectious diseases are often not random, but with direction. Hence, in this paper, we build epidemic model based on an interconnected directed network, which can be considered as the generalization of undirected networks and bipartite networks. By using the mean-field approach, we establish the Susceptible-Infectious-Susceptible model on this network. We theoretically analyze the model, and obtain the basic reproduction number, which is also the generalization of the critical number corresponding to undirected or bipartite networks. And we prove the global stability of disease-free and endemic equilibria via the basic reproduction number as a forward bifurcation parameter. We also give a condition for epidemic prevalence only on a single subnetwork. Furthermore, we carry out numerical simulations, and find that the independence between each nodes in- and out-degrees greatly reduce the impact of the networks topological structure on disease spread.
The recently proposed generalized epidemic modeling framework (GEMF) cite{sahneh2013generalized} lays the groundwork for systematically constructing a broad spectrum of stochastic spreading processes over complex networks. This article builds an algorithm for exact, continuous-time numerical simulation of GEMF-based processes. Moreover the implementation of this algorithm, GEMFsim, is available in popular scientific programming platforms such as MATLAB, R, Python, and C; GEMFsim facilitates simulating stochastic spreading models that fit in GEMF framework. Using these simulations one can examine the accuracy of mean-field-type approximations that are commonly used for analytical study of spreading processes on complex networks.
In recent years the research community has accumulated overwhelming evidence for the emergence of complex and heterogeneous connectivity patterns in a wide range of biological and sociotechnical systems. The complex properties of real-world networks have a profound impact on the behavior of equilibrium and nonequilibrium phenomena occurring in various systems, and the study of epidemic spreading is central to our understanding of the unfolding of dynamical processes in complex networks. The theoretical analysis of epidemic spreading in heterogeneous networks requires the development of novel analytical frameworks, and it has produced results of conceptual and practical relevance. A coherent and comprehensive review of the vast research activity concerning epidemic processes is presented, detailing the successful theoretical approaches as well as making their limits and assumptions clear. Physicists, mathematicians, epidemiologists, computer, and social scientists share a common interest in studying epidemic spreading and rely on similar models for the description of the diffusion of pathogens, knowledge, and innovation. For this reason, while focusing on the main results and the paradigmatic models in infectious disease modeling, the major results concerning generalized social contagion processes are also presented. Finally, the research activity at the forefront in the study of epidemic spreading in coevolving, coupled, and time-varying networks is reported.
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