# The effects of spatially-constrained treatment regions upon a model of wombat mange

## TL;DR

This study models how treating wombats in specific areas can reduce mange mites, but success depends on initial disease state and treatment location.

## Contribution

The paper introduces a spatially constrained treatment model for managing Sarcoptes scabiei in wombats using non-linear PDEs.

## Key findings

- Targeted treatment can reduce mite numbers in treatment regions and increase wombat populations.
- Treatment effectiveness depends on initial disease state and treatment location within the wombat population.
- Understanding host-pathogen dynamics and spatial terrain is crucial for successful treatment.

## Abstract

The use of therapeutic agents is a critical option to manage wildlife disease, but their implementation is usually spatially constrained. We seek to expand knowledge around the effectiveness of management of environmentally-transmitted Sarcoptes scabiei on a host population, by studying the effect of a spatially constrained treatment regime on disease dynamics in the bare-nosed wombat Vombatus ursinus. A host population of wombats is modelled using a system of non-linear partial differential equations, a spatially-varying treatment regime is applied to this population and the dynamics are studied over a period of several years. Treatment could result in mite decrease within the treatment region, extending to a lesser degree outside, with significant increases in wombat population. However, the benefits of targeted treatment regions within an environment are shown to be dependent on conditions at the start (endemic vs. disease free), as well as on the locations of these special regions (centre of the wombat population or against a geographical boundary). This research demonstrates the importance of understanding the state of the environment and populations before treatment commences, the effects of re-treatment schedules within the treatment region, and the transient large-scale changes in mite numbers that can be brought about by sudden changes to the environment. It also demonstrates that, with good knowledge of the host-pathogen dynamics and the spatial terrain, it is possible to achieve substantial reduction in mite numbers within the target region, with increases in wombat numbers throughout the environment.

The online version contains supplementary material available at 10.1007/s00285-024-02078-9.