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 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.
Highlights
This work is motivated by the need to develop a reliable and efficient method for detecting the presence and estimating population density of the invasive fruit fly, Bactrocera invadens Drew, Tsuruta & White (Diptera: Tephritidae) in South Africa
Parameter Identification is challenging, in particular when the direct problem is defined by PDEs, since it often leads to solving inverse problems that are illposed or ill-conditioned
This method enables the identification of parameter values that describe population characteristics, i.e the population density, its diffusion rate, attractiveness of the traps and their maximum radius of attraction
Summary
This work is motivated by the need to develop a reliable and efficient method for detecting the presence and estimating population density of the invasive fruit fly, Bactrocera invadens Drew, Tsuruta & White (Diptera: Tephritidae) in South Africa. Fruit flies are a perennial problem in South Africa because in addition to B. invadens there are three endemic species that already represent economic pests. Fruit flies have historically been controlled in South Africa by the application of insecticide cover sprays. With regard to B. invadens, male annihilation technique has been applied to control incursions in South Africa [21]. Another control strategy for this pest may include mass-trapping, which uses male attractants to capture and kill males of a population, leading to reduced female mating and possibly causing local extinction of the population [12].
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