Abstract

Modelling epidemics in tree populations can be addressed on a variety of scales and resolutions. Individual tree-to-tree interactions are responsible for all emergent epidemics through countries and continents, however, modelling all interactions over the whole population is presently unfeasible. To address this, we develop a sub-grid modelling framework combining two different models at different scales. The hybrid model uses a smaller scale Monte Carlo sub-grid model at resolution 5 m^{2 that informs a reactive-diffusive (RD) PDE model at resolution 1 km}2. The Monte Carlo sub-grid model is based on compartmentalised SIR with non-local dispersion and is shown to demonstrate travelling wave-like behaviour when ensemble-averaged. The RD PDE system chosen is the F-K-P-P (or Fisher Kolmogorov) model, the simplest model that demonstrates the propagation of travelling waves and logistic growth of the pathogen. From simple epidemiological input parameters and a (modelled) abundance dataset, the travelling wave-speeds of the sub-grid are predetermined and mapped to diffusion coefficients that inform the FKPP equation. The FKPP equation is then numerically simulated with a finite-difference method to approximate a pathogen spreading through UK tree population. This framework attempts to aid efforts in developing flexible, generalisable, large-scale epidemic models based on small scale epidemiological principles.