Simulating Disease in Periods of Low Mobility Using a Hybrid Diffusion and Compartmental Model Built on Geographic Data

Recent events relating to the Covid-19 Pandemic have increased the interest in modelling the spread of disease. This paper describes an approach to modelling the spread of a disease across Ireland using a hybrid compartmental and diffusion model built around small areas defined by the Central Statistics Office and Northern Ireland Statistics and Research Agency normally used to process National Census data. Voronoi diagrams are used to simplify the small region descriptions to polygons that provide a single linear boundary between each region. The progress of the disease within each region and between neighbouring regions was modelled using a hybrid SEIRD (Susceptible, Exposed, Infectious, Recovery, Death) and diffusion technique. The paper describes how the model can be fitted to data available for the current Covid-19 pandemic to simulate cases over periods of lockdown where individual mobility is low. The approach used also has potential application to model Ash die-back and the spread of invasive species.