Optimal control in a multistage physiologically structured insect population model

We present an age- and stage-structured population model to study some methods of control of one of the most important grapevine pests, the European grapevine moth. We consider control by insecticides that reduce either the proportion of surviving eggs, larvae or both, as well as chemicals that cause mating disruption, thereby reducing the number of eggs laid. We formulate optimal control problems with cost functionals related to real-life costs in the wine industry, and we prove that these problems admit a unique solution. We also provide some numerical examples from simulation.

[1]  C. Berry,et al.  Characterization of Bacillus thuringiensis isolates toxic to cotton boll weevil (Anthonomus grandis) , 2007 .

[2]  Michel Langlais,et al.  OPTIMAL CONTROL FOR A NONLINEAR AGE-STRUCTURED POPULATION DYNAMICS MODEL , 2002 .

[3]  Suzanne Lenhart,et al.  Optimal Harvesting in an Age-Structured Predator–Prey Model , 2006 .

[4]  Ya-Xin Li,et al.  Biological control: A guide to natural enemies in North America , 2003 .

[5]  S. Lenhart,et al.  Optimal control of a competitive system with age-structure , 2004 .

[6]  Ping Zhao,et al.  Optimal control of harvesting for age-dependent predator-prey system , 2005, Math. Comput. Model..

[7]  Delphine Picart,et al.  An innovative multistage, physiologically structured, population model to understand the European grapevine moth dynamics , 2011 .

[8]  Bedr'Eddine Ainseba,et al.  Parameter identification in multistage population dynamics model , 2011 .

[9]  Vassilis A. Vassiliou,et al.  Control of Lobesia botrana (Lepidoptera: Tortricidae) in vineyards in Cyprus using the Mating Disruption Technique , 2009 .

[10]  S. Matucci,et al.  A problem of optimal harvesting policy in two-stage age-dependent populations. , 1997, Mathematical biosciences.

[11]  A. Shelton,et al.  Biological control; [computer file] ; a guide to natural enemies in North America /; Catherine R. Weeden, Anthony M. Shelton, and Michael P. Hoffmann, editors. , 2000 .

[12]  I. Ekeland.  On the variational principle , 1974 .

[13]  Suzanne Lenhart,et al.  Optimal control of boundary habitat hostility for interacting species , 1999 .

[14]  Delphine Picart.  Modélisation et estimation des paramètres liés au succès reproducteur d'un ravageur de la vigne (Lobesia botrana DEN. & SCHIFF.) , 2009 .

[15]  Bedr'Eddine Ainseba,et al.  Optimal control problem on insect pest populations , 2011, Appl. Math. Lett..

[16]  J. Cross,et al.  Exploitation of the sex pheromone of apple leaf midge Dasineura mali Kieffer (Diptera: Cecidomyiidae) for pest monitoring: Part 1. Development of lure and trap , 2009 .

[17]  S. Lenhart,et al.  Harvesting control in an integrodifference population model with concave growth term , 2007 .

[18]  Mimmo Iannelli,et al.  Optimal Control of Population Dynamics , 1999 .

[19]  Denis Thiéry,et al.  Relative performance of European grapevine moth (Lobesia botrana) on grapes and other hosts , 2005, Oecologia.