GIS-ODE: linking dynamic population models with GIS to predict pathogen vector abundance across a country under climate change scenarios.

Mechanistic mathematical models such as ordinary differential equations (ODEs) have a long history for their use in describing population dynamics and determining estimates of key parameters that summarize the potential growth or decline of a population over time. More recently, geographic information systems (GIS) have become important tools to provide a visual representation of statistically determined parameters and environmental features over space. Here, we combine these tools to form a 'GIS-ODE' approach to generate spatiotemporal maps predicting how projected changes in thermal climate may affect population densities and, uniquely, population dynamics of Ixodes ricinus, an important tick vector of several human pathogens. Assuming habitat and host densities are not greatly affected by climate warming, the GIS-ODE model predicted that, even under the lowest projected temperature increase, I. ricinus nymph densities could increase by 26-99% in Scotland, depending on the habitat and climate of the location. Our GIS-ODE model provides the vector-borne disease research community with a framework option to produce predictive, spatially explicit risk maps based on a mechanistic understanding of vector and vector-borne disease transmission dynamics.