Dynamics of epidemic spreading on connected graphs

Besse, Christophe; Faye, Grégory

doi:10.1007/s00285-021-01602-5

Cited by 11 publications

(9 citation statements)

References 32 publications

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“…We see this work as a first step towards a more systematic understanding of spreading phenomena in more realistic and practical networks, such as transportation networks for example [10]. In a very recent work [5], we proposed a new model that describes the dynamics of epidemic spreading on connected graphs. Our model consists in a PDE/ODE system where at each vertex of the graph we have a standard SIR model and connections between vertices are given by heat equations on the edges supplemented with Robin like boundary conditions at the vertices modeling exchanges between incident edges and the associated vertex.…”

Section: Discussionmentioning

confidence: 99%

“…Our model consists in a PDE/ODE system where at each vertex of the graph we have a standard SIR model and connections between vertices are given by heat equations on the edges supplemented with Robin like boundary conditions at the vertices modeling exchanges between incident edges and the associated vertex. Under some appropriate scaling assumptions, the model of the present paper can be seen as the limit of the PDE/ODE model from [5]. One of our objective will be to understand how the spreading properties analyzed here can be transposed to this extended PDE/ODE model.…”

Section: Discussionmentioning

confidence: 99%

“…SIR models on graphs with similar exchanges of infected individuals have previously been introduced in the literature [10,[14][15][16]20] with a particular emphasis on spreading properties. Actually, model (1.1) is at the crossroad of traditional reaction-diffusion models on graphs [11,23] and epidemic models that incorporate more sophisticated interactions dynamics [2,5,8,9,22,[26][27][28]. Note that in (1.1), we have assumed that only the infected population is subject to diffusion within the graph, and we think of S v being an ambient population whose movement does not affect its distribution.…”

Section: Introductionmentioning

confidence: 99%

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Spreading properties for SIR models on homogeneous trees

Besse¹,

Faye²

2021

Preprint

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We consider an epidemic model of SIR type set on a homogeneous tree and investigate the spreading properties of the epidemic as a function of the degree of the tree, the intrinsic basic reproduction number and the strength of the interactions within the population of infected individuals. When the degree is one, the homogeneous tree is nothing but the standard lattice on the integers and our model reduces to a SIR model with discrete diffusion for which the spreading properties are very similar to the continuous case. On the other hand, when the degree is larger than two, we observe some new features in the spreading properties. Most notably, there exists a critical value of the strength of interactions above which spreading of the epidemic in the tree is no longer possible.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Spreading properties for SIR models on homogeneous trees

Besse¹,

Faye²

2021

Preprint

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“…Noble [1974], added diffusion terms to the balance equations for both Susceptible and Infected persons of basic SIR model. This converts these two equations to time-dependent partial differential equations (PDE) Recently Besse and Faye [2021] used diffusion equation to account for migration of (only) infected individuals on connected graphs, a system of cities connected by a transportation network. This converts the infected (I) population equation for each node (city) to a non-linear PDE, coupling the neighbouring parts of the transportation network The equations for Susceptible (S) and Removed (R) groups remain the non-linear ODE.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modelling of Multi-Region Spread of Epidemic

Sahni

Türeci

2022

Preprint

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SAIR model of growth of an epidemic is extended to a system of many interacting regions. Interactions are described by exchange of populations between various regions. Differences caused by the exchange of susceptible population, in addition to infected individuals are noted. It is shown that initial phase of the epidemic is governed by a linear system. Analysis of linear system shows that a fundamental mode gets established that governs the spatial profile of the spread of the disease.

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“…We introduce a discrete modeling framework for simulating gradient-driven advection-dispersion-reaction physics of multispecies transport. Graph-theoretic approaches that have been proven successful in examining flow of information through large-scale real-world networks are applied (Kumar et al, 2019;Bellocchi and Geroliminis, 2020;Besse and Faye, 2021) in this study. We resort to discrete-vector calculus and use the operators defined on a finite-graph to spatially discretize and formulate the transport dynamics in the vascular domain as a "tank-in-series" model.…”

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confidence: 99%

A Graph-Based Framework for Multiscale Modeling of Physiological Transport

Maheshvare

Raha

Pal

2022

Front. Netw. Physiol.

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Trillions of chemical reactions occur in the human body every second, where the generated products are not only consumed locally but also transported to various locations in a systematic manner to sustain homeostasis. Current solutions to model these biological phenomena are restricted in computability and scalability due to the use of continuum approaches in which it is practically impossible to encapsulate the complexity of the physiological processes occurring at diverse scales. Here, we present a discrete modeling framework defined on an interacting graph that offers the flexibility to model multiscale systems by translating the physical space into a metamodel. We discretize the graph-based metamodel into functional units composed of well-mixed volumes with vascular and cellular subdomains; the operators defined over these volumes define the transport dynamics. We predict glucose drift governed by advective–dispersive transport in the vascular subdomains of an islet vasculature and cross-validate the flow and concentration fields with finite-element–based COMSOL simulations. Vascular and cellular subdomains are coupled to model the nutrient exchange occurring in response to the gradient arising out of reaction and perfusion dynamics. The application of our framework for modeling biologically relevant test systems shows how our approach can assimilate both multi-omics data from in vitro–in vivo studies and vascular topology from imaging studies for examining the structure–function relationship of complex vasculatures. The framework can advance simulation of whole-body networks at user-defined levels and is expected to find major use in personalized medicine and drug discovery.

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Dynamics of epidemic spreading on connected graphs

Cited by 11 publications

References 32 publications

Spreading properties for SIR models on homogeneous trees

Spreading properties for SIR models on homogeneous trees

Mathematical Modelling of Multi-Region Spread of Epidemic

A Graph-Based Framework for Multiscale Modeling of Physiological Transport

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