Time Dependent Diffusion as a Mean Field Counterpart of Levy Type Random Walk

Insect trapping is commonly used in various pest insect monitoring programs as well as in many ecological field studies. An individual is said to be trapped if it falls within a well defined capturing zone, which it cannot escape. The accumulation of trapped individuals over time forms trap counts or alternatively, the flux of the population density into the trap. In this paper, we study the movement of insects whose dynamics are governed by time dependent diffusion and Lévy walks. We demonstrate that the diffusion model provides an alternative framework for the Cauchy type random walk (Lévy walk with Cauchy distributed steps). Furthermore, by calculating the trap counts using these two conceptually different movement models, we propose that trap counts for pests whose dynamics may be Lévy by nature can effectively be predicted by diffusive flux curves with time-dependent diffusivity.