The effect of spatial dynamics on the behaviour of an environmentally transmitted disease

Abstract

Understanding the spread of pathogens through the environment is critical to a fuller comprehension of disease dynamics. However, many mathematical models of disease dynamics ignore spatial effects. We seek to expand knowledge around the interaction between the bare-nosed wombat (Vombatus ursinus) and sarcoptic mange (etiologic agent Sarcoptes scabiei), by extending an aspatial mathematical model to include spatial variation. S. scabiei was found to move through our modelled region as a spatio-temporal travelling wave, leaving behind pockets of localized host extinction, consistent with field observations. The speed of infection spread was also comparable with field research. Our model predicts that the inclusion of spatial dynamics leads to the survival and recovery of affected wombat populations when an aspatial model predicts extinction. Collectively, this research demonstrates how environmentally transmitted S. scabiei can result in travelling wave dynamics, and that inclusion of spatial variation reveals a more resilient host population than aspatial modelling approaches.