A coupled spatial-network model: A mathematical framework for applications in epidemiology
by Hannah Kravitz, Christina Durón, and Moysey Brio
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A new compartmental modeling framework is proposed which couples population centers at the vertices, 1D travel routes on the edges, and a 2D continuum containing the rest of the population to simulate how an infection spreads through a population. The edge equations are coupled to the vertex ODEs through junction conditions, while the domain equations are coupled to the edges through boundary conditions. The model is illustrated on some example geometries, and a parameter study example is performed. The observed solutions exhibit exponential decay after a certain time has passed, and the cumulative infected population over the vertices, edges, and domain tends to a constant in time but varying in space, i.e., a steady state solution.
Example implementation of the coupled spatial-network model.
