Abstract:
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 trap insects
at different rates. 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 a suitable
advection term defined by the active area of the traps.
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.
