Document Type : Review articles
Department of Mathematics, Mbarara University of Science and Technology, P.O.Box 1410, Mbarara, Uganda.
Bioversity International-Uganda, P.O.Box 24384, Naguru, Kampala, Uganda.
A mathematical model for the control of the banana weevil Cosmopolites Sordidus (Germar) by predatory ant species is formulated and analyzed. The model incorporates predator switching to a non-dynamic alternative food source, optimal foraging theory and self regulation in both the banana weevil and predatory-ant species! Using Lyapunov's first method, the local stability of the equilibria is established. Furthermore, conditions for the existence of the interior equilibrium are derived and its global stability established by the Bendixson--Dulac criterion with periodic orbits ruled out by the Poincare--Bendixson theorem. It is determined that intrinsic growth rates and carrying capacities rather than handling time and nutritional value have significant impact on the banana weevils-- predatory ant interaction. Numerical simulations confirm the theoretical results.