Optimal Control of Gypsy Moth Populations

Abstract

This study investigates an optimal strategy for the cost effective control of gypsy moth populations. Gypsy moth populations cycle between low sparse numbers to high outbreak levels and it is during the outbreak levels that the moths cause extensive damage to plant foliage which can lead to deforestation. Deforestation can result in significant economic damage to infested areas, and consequently, there have been many efforts to control moth populations. One effective method of control is the use of the biocontrol agent, Gypchek, but its production is costly. We develop a mathematical model which combines population dynamics and optimal control of the moth population to explore strategies by which the total cost of the gypsy moth problem (economic damage and cost of Gypchek) can be minimized.

Identification and Knockdown of the Olfactory Receptor (OrCo) in Gypsy Moth, Lymantria dispar

“…This paper focuses on the gypsy moth, Lymantria dispar , an economically important insect that can severely disrupt forested ecosystems worldwide. The gypsy moth population cycle rises and falls, alternating between low numbers and large-scale outbreaks; during outbreaks, the moths cause extensive damage to plant foliage that can lead to massive tree death 1. Most insect behaviors, such as mating, feeding, and nesting, are closely related to olfaction.…”

Discrete-time host–parasitoid models with pest control

“…Due to the simple asymptotic dynamics of the Beverton-Holt nonlinearity, we obtain consistent results for the optimal control problems. Notice that the Ricker type nonlinearity has been adopted as a gypsy moth's growth rate in a study conducted by Whittle et al [26], where virus is used as a biological control in their study. For the Ricker nonlinearity, we choose parameter r in regimes corresponding to different dynamical behaviours of the host population in the absence of the parasitoid and the control.…”

“…Furthermore, gypsy moth populations in the northeastern US exhibit eruptive population dynamics which result in extensive tree defoliation and ultimately deforestation. Whittle et al [26] use a discrete-time optimal control model to investigate the effects of the manufactured Nucleopolyhedrosis Virus (NPV) (Gypchek) sprayed on the moth. Whittle et al [26] also use the Ricker type nonlinearity to model moth's per capita growth rate.…”

“…Whittle et al [26] use a discrete-time optimal control model to investigate the effects of the manufactured Nucleopolyhedrosis Virus (NPV) (Gypchek) sprayed on the moth. Whittle et al [26] also use the Ricker type nonlinearity to model moth's per capita growth rate. On the other hand, since Beverton-Holt nonlinearity frequently appears in the literature and is a classical example for contest intraspecific competition, we also investigate the model with Beverton-Holt growth rate.…”

Optimal control of integrodifference equations in a pest-pathogen system

“…We start with constant initial conditions for both gypsy moth and the virus. Some of the parameters (γ, ρ, f ) are taken from previous work [57,19,69], while others (r, b) are adjusted so that model solutions exhibit the characteristic oscillatory behavior of gypsy moth populations. In Figure 1 we can observe two interesting results when the initial spatial distributions for both moth and virus are constant.…”