Mathematical modelling of the biological pest control of the sugarcane borer

Abstract

In this paper, we propose a simple mathematical model of interaction between the sugarcane borer (Diatraea saccharalis) and its egg parasitoid Trichogramma galloi. In this model, the sugarcane borer is represented by the egg and the larval stages, and the parasitoid is considered in terms of the parasitized eggs. Linear feedback control strategy is proposed to indicate how the natural enemies should be introduced into the environment.

Keywords:

• mathematical modelling
• biological control
• sugarcane borer
• egg parasitoid
• optimal control problem

2000 AMS Subject Classifications :

• 92D25
• 34H15
• 49N90

Acknowledgements

This work has been financed by Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) and Conselho Nacional de Pesquisas (CNPq). Finally, the authors are grateful to the anonymous referees for their valuable comments.