On the population dynamics of the Australian bushfly

Each spring, the Australian bushfly ( Musca vetustissima Walker) migrates from its over-wintering areas located in central Australia and repopulates the south-eastern parts of the continent. In this paper, a simple size-structured model, in the form of a reaction–advection equation with delay, is presented for the evolution of the population density of the bushfly. The model takes into account the important role of cattle dung in its life cycle and includes the effects of wind-borne migration. Bifurcation analyses of the model equations in the absence of wind advection reveals the environmental conditions under which the fly population will die out, reach a stable equilibrium or explode. Numerical simulations which include advection reveal the importance of wind-borne migration in building up the population of flies in south-eastern Australia during the summer months.