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

Multiple endemic equilibria in an environmentally-transmitted disease with three disease stages

We construct, analyze and interpret a mathematical model for an environmental transmitted disease characterized for the existence of three disease stages: acute, severe and asymptomatic. Besides, we consider that severe and asymptomatic cases may present relapse between them. Transmission dynamics driven by the contact rates only occurs when a parameter R∗>1, as normally occur in directly-transmitted or vector-transmitted diseases, but it will not adequately correspond to a basic reproductive number as it depends on environmental parameters. In this case, the forward transcritical bifurcation that exists for R∗<1, becomes a backward bifurcation, producing multiple steady-states, a hysteresis effect and dependence on initial conditions. A threshold parameter for an epidemic outbreak, independent of R∗ is only the ratio of the external contamination inflow shedding rate to the environmental clearance rate. R∗ describes the strength of the transmission to infectious classes other than the I-(acute) type infections. The epidemic outbreak conditions and the structure of R∗ appearing in this model are both responsible for the existence of endemic states.

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

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.

Pharmacokinetic and pharmacodynamic considerations for treating sarcoptic mange with cross-relevance to Australian wildlife

Sarcoptes scabiei is the microscopic burrowing mite responsible for sarcoptic mange, which is reported in approximately 150 mammalian species. In Australia, sarcoptic mange affects a number of native and introduced wildlife species, is particularly severe in bare-nosed wombats (Vombatus ursinus) and an emerging issue in koala and quenda. There are a variety of acaricides available for the treatment of sarcoptic mange which are generally effective in eliminating mites from humans and animals in captivity. In wild populations, effective treatment is challenging, and concerns exist regarding safety, efficacy and the potential emergence of acaricide resistance. There are risks where acaricides are used intensively or inadequately, which could adversely affect treatment success rates as well as animal welfare. While reviews on epidemiology, treatment strategies, and pathogenesis of sarcoptic mange in wildlife are available, there is currently no review evaluating the use of specific acaricides in the context of their pharmacokinetic and pharmacodynamic properties, and subsequent likelihood of emerging drug resistance, particularly for Australian wildlife. This review critically evaluates acaricides that have been utilised to treat sarcoptic mange in wildlife, including dosage forms and routes, pharmacokinetics, mode of action and efficacy. We also highlight the reports of resistance of S. scabiei to acaricides, including clinical and in vitro observations.