Influence of Intrapredatory Interferences on Impulsive Biological Control Efficiency

Sapna Nundloll 1 Ludovic Mailleret 1, 2 Frédéric Grognard 1
1 COMORE - Modeling and control of renewable resources
LOV - Laboratoire d'océanographie de Villefranche, CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : In this paper, a model is proposed for the biological control of a pest by its natural predator. The model incorporates a qualitative description of intrapredatory interference whereby predator density decreases the per capita predation efficiency and generalises the classical Beddington-DeAngelis formulation. A pair of coupled ordinary differential equations are used, augmented by a discrete component to depict the periodic release of a fixed number of predators into the system. This number is defined in terms of the rate of predator release and the frequency at which the releases are to be carried out. This formulation allows us to compare different biological control strategies in terms of release size and frequency that involve the same overall number of predators. The stability properties of the zero-pest solution are analysed. We obtain an upper bound on the interference strength (the biological condition) and a minimal bound on the predator release rate (the managerial condition) required to eradicate a pest population. We demonstrate that increasing the frequency of releases reduces this minimal rate and also increases the rate of convergence of the system to the zero-pest solution for a given release rate. Additionally, we show that other conclusions are to be expected if the interferences between predators have weaker or stronger effects than the generalised Beddington-DeAngelis formulation proposed in this paper.
Type de document :
Article dans une revue
Bulletin of Mathematical Biology, Springer Verlag, 2010, 72 (8), pp.2113-2138. 〈10.1007/s11538-010-9531-6〉
Liste complète des métadonnées

Littérature citée [43 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/hal-00847302
Contributeur : Jean-Luc Gouzé <>
Soumis le : mardi 23 juillet 2013 - 11:23:41
Dernière modification le : jeudi 11 janvier 2018 - 16:49:53
Document(s) archivé(s) le : jeudi 24 octobre 2013 - 10:10:31

Fichier

nundloll_BMB2010.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

Citation

Sapna Nundloll, Ludovic Mailleret, Frédéric Grognard. Influence of Intrapredatory Interferences on Impulsive Biological Control Efficiency. Bulletin of Mathematical Biology, Springer Verlag, 2010, 72 (8), pp.2113-2138. 〈10.1007/s11538-010-9531-6〉. 〈hal-00847302〉

Partager

Métriques

Consultations de la notice

538

Téléchargements de fichiers

177