Partial differential equation models for invasive species spread in the presence of spatial heterogeneity.

Models of invasive species spread often assume that landscapes are spatially homogeneous; thus simplifying analysis but potentially reducing accuracy. We extend a recently developed partial differential equation model for invasive conifer spread to account for spatial heterogeneity in parameter values and introduce a method to obtain key outputs (e.g. spread rates) from computational simulations. Simulations produce patterns of spatial spread which appear qualitatively similar to observed patterns in grassland ecosystems invaded by exotic conifers, validating our spatially explicit strategy. We find that incorporating spatial variation in different parameters does not significantly affect the evolution of invasions (which are characterised by a long quiescent period followed by rapid evolution towards to a constant rate of invasion) but that distributional assumptions can have a significant impact on the spread rate of invasions. Our work demonstrates that spatial variation in site-suitability or other parameters can have a significant impact on invasions and must be considered when designing models of invasive species spread.

Predicting elimination of evolving virus variants.

As the SARS-CoV-2 virus spreads around the world new variants are appearing regularly. Although some countries have achieved very swift and successful vaccination campaigns, on a global scale the vast majority of the population is unvaccinated and new variants are proving more resistant to the current set of vaccines. We present a simple model of disease spread, which includes the evolution of new variants of a novel virus and varying vaccine effectiveness to these new strains. We show that rapid vaccine updates to target new strains are more effective than slow updates and containing spread through non-pharmaceutical interventions is vital while these vaccines are delivered. Finally, when measuring the key model inputs, e.g. the rate at which new mutations and variants of concern emerge, is difficult we show how an observable model output, the number of new variants that have been seen, is strongly correlated with the probability the virus is eliminated.