Extinction Conditions from a One-Sided Competition Model with a Holling Type I Functional Response for the Sterile Insect Technique

Yassine Chargui,Adel Trabelsi,Anis Dhahbi

doi:10.4236/ojmsi.2018.62002

Yassine Chargui, Adel Trabelsi + Show 1 more

Open Access

https://doi.org/10.4236/ojmsi.2018.62002

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Abstract

The Sterile Insect Technique (SIT) is a powerful biological tool to control pest-populations. It could be integrated in management programmes of the Red Palm Weevil (RPW) Rhynchophorus ferrugineus Olivier. This pest threatens seriously date palms particularly in Saudi Arabia. As a matter of fact, the use of SIT has been very efficient in controlling RPW populations in coconut gardens in various countries. In this work, we outline the extinction conditions of a target wild-population using a one-sided competition model to describe its competition with released sterile insects. We employ a Holling type I functional response to describe the sterile-fertile one-sided competition and we consider two intra-specific competition sub-models, with and without Allee Effect, in modelling the growth of the wild-type population. We also study two manners of liberating sterile insects: single and periodic release strategies.

Highlights

IntroductionThe Red Palm Weevil (RPW)Rhynchophorus ferrugineus Olivier is a notorious pest with a worldwide range and a history of fast spread and painful invasions to various countries, especially in the Arabian Peninsula [1] [2] [3]
The Sterile Insect Technique (SIT) is a powerful biological tool to control pest-populations. It could be integrated in management programmes of the Red Palm Weevil (RPW) Rhynchophorus ferrugineus Olivier
The Red Palm Weevil (RPW)Rhynchophorus ferrugineus Olivier is a notorious pest with a worldwide range and a history of fast spread and painful invasions to various countries, especially in the Arabian Peninsula [1] [2] [3]

Summary

Introduction

The Red Palm Weevil (RPW)Rhynchophorus ferrugineus Olivier is a notorious pest with a worldwide range and a history of fast spread and painful invasions to various countries, especially in the Arabian Peninsula [1] [2] [3]. The SIT method introduced by Knipling [11] [12] in 1930s, with a species-specific area-wide, is relying on the insect rearing, the sterilization without affecting the mating ability, and the release of a specific numbers of insects [11] [13]. The minimal size of sterile males to be released in order to achieve the extinction of the pest population will be determined for different strategies. This aids in estimating the cost of applying the SIT program.

The Mathematical Model

Logistic Sub-Model

Including Allee Effect

Conclusions