Effects of local population structure in a reaction-diffusion model of a contact process on metapopulation networks

Mata, Angélica S.; Ferreira, Silvio C.; Pastor-Satorras, Romualdo

doi:10.1103/physreve.88.042820

Cited by 25 publications

(26 citation statements)

References 43 publications

(81 reference statements)

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“…These models generally assume homogeneous mixing within patches where the infection dynamics takes place (or mixing between population groups [47]) and either an effective coupling between patches or explicit migration/mobility processes. While non-Markovian rules have been introduced in migration processes in metapopulation models for the study of disease spread and epidemic threshold conditions [48][49][50][51], explicit contact structure between individuals in a patch have been rarely considered [52], assuming static topologies. Our approach thus differs from usual metapopulation models in that it provides explicit temporally evolving contact structures within each group, allowing for different possible dynamics of mobility and contacts.…”

Section: Agent-based Model Of Interaction Dynamicsmentioning

confidence: 99%

Impact of spatially constrained sampling of temporal contact networks on the evaluation of the epidemic risk

Vestergaard¹,

Valdano²,

Génois³

et al. 2016

Eur. J. Appl. Math

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International audienceThe ability to directly record human face-to-face interactions increasingly enables the development of detailed data-driven models for the spread of directly transmitted infectious diseases at the scale of individuals. Complete coverage of the contacts occurring in a population is however generally unattainable, due for instance to limited participation rates or experimental constraints in spatial coverage. Here, we study the impact of spatially constrained sampling on our ability to estimate the epidemic risk in a population using such detailed data-driven models. The epidemic risk is quantified by the epidemic threshold of the SIRS model for the propagation of communicable diseases, i.e. the critical value of disease transmissibility above which the disease turns endemic. We verify for both synthetic and empirical data of human interactions that the use of incomplete data sets due to spatial sampling leads to the underestimation of the epidemic risk. The bias is however smaller than the one obtained by uniformly sampling the same fraction of contacts: it depends non-linearly on the fraction of contacts that are recorded, and becomes negligible if this fraction is large enough. Moreover, it depends on the interplay between the timescales of population and spreading dynamics

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Section: Agent-based Model Of Interaction Dynamicsmentioning

confidence: 99%

Impact of spatially constrained sampling of temporal contact networks on the evaluation of the epidemic risk

Vestergaard¹,

Valdano²,

Génois³

et al. 2016

Eur. J. Appl. Math

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“…Using heterogeneous mean-field (HMF) theory and assuming that subpopulations with the same degree are statistical equivalent, Colizza and Vespignani proposed two models to describe transmission of diseases on heterogeneous metapopulation networks under two different mobility patterns, which sheds light on calculation of global invasion threshold [7] . Next, different network structures, including bipartite metapopulation network [8] , time-varying metapopulation network [9] , local subpopulation structure [10] , interconnected metapopulation network [11] , have been found to play an essential role in the global spread of infectious diseases. Furthermore, studies have shown that adaptive behavior of individuals contributes to the global spread of epidemics, contrary to willingness [12][13][14][15] .…”

Section: Introductionmentioning

confidence: 99%

Infectious diseases spreading on a metapopulation network coupled with its second-neighbor network

Feng

Jin

2019

Applied Mathematics and Computation

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a b s t r a c tTraditional infectious diseases models on metapopulation networks focus on direct transportations (e.g., direct flights), ignoring the effect of indirect transportations. Based on global aviation network, we turn the problem of indirect flights into a question of second neighbors, and propose a susceptible-infectious-susceptible model to study disease transmission on a connected metapopulation network coupled with its second-neighbor network (SNN). We calculate the basic reproduction number, which is independent of human mobility, and we prove the global stability of disease-free and endemic equilibria of the model. Furthermore, the study shows that the behavior that all travelers travel along the SNN may hinder the spread of disease if the SNN is not connected. However, the behavior that individuals travel along the metapopulation network coupled with its SNN contributes to the spread of disease. Thus for an emerging infectious disease, if the real network and its SNN keep the same connectivity, indirect transportations may be a potential threat and need to be controlled. Our work can be generalized to high-speed train and rail networks, which may further promote other research on metapopulation networks.

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“…Relevance of the interplay between diffusion and epidemic spreading in real systems is self-evident since hosts of infectious agents, such as people and mobile devices, are constantly moving and being the carriers that promote the quick transition from a localized outbreak to a large scale epidemics 4,5,15 . Diffusion has been investigated on networks for bosonic epidemic processes where the vertices can be simultaneously occupied by several individuals 18 and, in particular, within the context of heterogeneous metapopulations [19][20][21][22][23] where each vertex consists itself of a subpopulation and the edges represent possibility of interchange of individuals moving from one subpopulation to another according to a mobility rule. When infected and healthy individuals move with the same rate on a metapopulation, the concentration of both types is proportional to the vertex degree 20 .…”

Section: Introductionmentioning

confidence: 99%

Activation thresholds in epidemic spreading with motile infectious agents on scale-free networks

Silva

Ferreira²

2018

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We investigate a fermionic susceptible-infected-susceptible model with mobility of infected individuals on uncorrelated scale-free networks with power-law degree distributions P (k) ∼ k −γ of exponents 2 < γ < 3. Two diffusive processes with diffusion rate D of an infected vertex are considered. In the standard diffusion, one of the nearest-neighbors is chosen with equal chance while in the biased diffusion this choice happens with probability proportional to the neighbor's degree. A non-monotonic dependence of the epidemic threshold on D with an optimum diffusion rate D * , for which the epidemic spreading is more efficient, is found for standard diffusion while monotonic decays are observed in the biased case. The epidemic thresholds go to zero as the network size is increased and the form that this happens depends on the diffusion rule and degree exponent. We analytically investigated the dynamics using quenched and heterogeneous mean-field theories. The former presents, in general, a better performance for standard and the latter for biased diffusion models, indicating different activation mechanisms of the epidemic phases that are rationalized in terms of hubs or max k-core subgraphs.Nowadays, we live in an interwoven world where information, goods, and people move through a complex structure with widely diversified types of interactions such as on-line friendship and airport connections. These and many other systems of completely distinct nature can be equally suited in a theoretical representation called complex networks, in which the elements are represented by vertices and the interactions among them by edges connecting these vertices.The study of epidemic processes on complex networks represents one of the cornerstones in modern network science and can aid the prevention (or even stimulation) of disease or misinformation spreading. The relevance of the interplay between diffusion and epidemic spreading in real systems is self-evident since hosts of infectious agents, such as people and mobile devices, are constantly moving, being the carriers that promote the quick transition from a localized outbreak to a large scale epidemic scenario. In this work, we perform a theoretical analysis and report nontrivial roles played by mobility of infected agents on the efficiency of epidemic spreading running on the top of complex networks. We expect that our results will render impacts for forthcoming research related to the area.

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Effects of local population structure in a reaction-diffusion model of a contact process on metapopulation networks

Cited by 25 publications

References 43 publications

Impact of spatially constrained sampling of temporal contact networks on the evaluation of the epidemic risk

Impact of spatially constrained sampling of temporal contact networks on the evaluation of the epidemic risk

Infectious diseases spreading on a metapopulation network coupled with its second-neighbor network

Activation thresholds in epidemic spreading with motile infectious agents on scale-free networks

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