Mathematical Characterization of Biological Control of Cassava Pests Model

Abstract

Pests are major constraints to the effective growth and development of every crop through their damage, and can be controlled effectively by the use of their natural enemies which is referred to as the biological pest control. In this study, the biological control model of cassava pests through optimal control theory was presented in order to minimize the population of the pests and stabilize the natural enemies population so as not to affect the crop negatively. A mathematical model was formulated via the Lotka-Volterra model, and the model was characterized. The optimality system was established, the equilibrium point with its uniqueness was established for the model. Finally, stability analysis of the model was investigated through optimal control approach and numerical data were employed to validate the system. The results obtained showed that cassava pests can be effectively controlled biologically.

Keywords: Optimal control, Cassava pest, Biological control, Stability, Natural enemies.