Mathematical modelling of koalas' home range

Urbanisation is rapidly expanding throughout natural habitat in which animals live. Particularly, in Eastern Australia, developments of infrastructure and suburbs have led to a significant decline in koala populations and altered animals’ home range dynamics. In a fragmented habitat, koalas face various threats that put their life at risk, such as vehicle collisions and domestic dog attacks. Similarly, changes in the climate threatens marsupials’ habitats because of an increase chance of draughts, bushfires and desertification dynamics. Understanding the behaviour that underlies koalas’ spatial distribution is fundamental to develop conservation strategies for the species. Using an original system of advection diffusion equations to model and predict koala spatial distribution, we investigate non-linear PDEs and ODEs to quantify the movements of two koalas coexisting in the same domain. General dynamics of steady states and transients are obtained via numerical method, while an analytical solution is provided for specific scenarios. We analysed various cases in which two koalas initiate their movement from the same location or from different positions and with different motilities. Our results represent the first mathematical description of koalas’ interactions in the same area, characterising conditions for avoidance, play, foraging and mating. The model proposed is the foundation for more complex ethological and ecological frameworks for marsupials in the wild.