Parameter Identification in Population Models for Insects Using Trap Data
Keywords:partial differential equation, advection-diffusion equation, parameter identification, inverse problem, trap interference, population density.
Traps are used commonly to establish the presence and population density of pest insects. Deriving estimates of population density from trap data typically requires knowledge of the properties of the trap (e.g. active area, strength of attraction) as well as some properties of the population (e.g. diffusion rate). These parameters are seldom exactly known, and also tend to vary in time, (e.g. as a result of changing weather conditions, insect physiological condition). We propose using a set of traps in such a configuration that they have different rate of trapping the insects. The properties of the traps and the characteristics of the population, including its density, are simultaneously estimated from the insects captured in these traps. The basic model is an advection-diffusion equation where the traps are represented via suitable advection term defined on the active area of the trap. The values of the unknown parameters of the model are derived by solving an optimization problem. Numerical simulations demonstrate the accuracy and the robustness of this method of parameter identification.
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