Dynamics of epidemic spreading on connected graphs

by   Christophe Besse, et al.

We propose 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 connexions 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. We describe the main properties of the system, and also derive the final total population of infected individuals. We present a semi-implicit in time numerical scheme based on finite differences in space which preserves the main properties of the continuous model such as the uniqueness and positivity of solutions and the conservation of the total population. We also illustrate our results with a selection of numerical simulations for a selection of connected graphs.



There are no comments yet.


page 35

page 42


Constructing minimally 3-connected graphs

A 3-connected graph is minimally 3-connected if removal of any edge dest...

A non-standard numerical scheme for an age-of-infection epidemic model

We propose a numerical method for approximating integro-differential equ...

Sums of Distances on Graphs and Embeddings into Euclidean Space

Let G=(V,E) be a finite, connected graph. We consider a greedy selection...

Graphical Construction of Spatial Gibbs Random Graphs

We present a Spatial Gibbs Random Graphs Model that incorporates the int...

Numerical Integration on Graphs: where to sample and how to weigh

Let G=(V,E,w) be a finite, connected graph with weighted edges. We are i...

Phase-field dynamics with transfer of materials: The Cahn–Hillard equation with reaction rate dependent dynamic boundary conditions

The Cahn–Hilliard equation is one of the most common models to describe ...

Constructing transient amplifiers for death-Birth updating: A case study of cubic and quartic regular graphs

A central question of evolutionary dynamics on graphs is whether or not ...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.