Parameter Identification in Population Models for Insects Using Trap Data

Abstract

BIOMATH h t t p : / / w w w. b i o m a t h f o r u m . o r g / b i o m a t h / i n d e x . p h p / b i o m a t h /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.

A Computer Model of Insect Traps in a Landscape

“…It is similar in spirit to another recent model26, which was motivated by the spread of Bactrocera fruit flies in Africa. Dufourd and colleagues examine the question of trap placement optimization, an important practical question that the current study could also inform.…”

Mathematical model for pest–insect control using mating disruption and trapping

“…Then, the right hand sides of (18) and (20) are the same at EE # . This implies that EE # is an equilibrium of (20).…”

“…When γM > Y + Y P , system (17) is reduced to system(18) and it can be written asẋ= R(x) − T (x), + µ I )I (ν Y + µ Y )Y − rν I I − δF (δ + µ F )F − ν Y Y µ M M − (1 − r)ν I I…”

Bounds on Absolute Gypsy Moth (Lymantria dispar dispar) (Lepidoptera: Erebidae) Population Density as Derived from Counts in Single Milk Carton Traps

“…Traps are utilized to detect and delimit small isolated insect populations and to estimate abundance and periods of activity [ 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 ]. Extensive research has been conducted over the years to establish the range of trap attraction, evaluate trap efficiency, estimate effective sampling area and catch probability, with the ultimate goal of interpreting trap catches and relating them to the actual population density [ 19 , 20 , 21 , 22 , 23 , 24 , 25 ]. Recent research by Bau and Cardé [ 26 ] demonstrated a high probability of false-negative trap catches when the density of an insect population is low and concluded that trap efficiency had a profound effect on detectability.…”