Theoretical framework for biological control of pest: a mathematical modeling approach

Crop losses to pests were the main obstacle to food security globally. Pest control was a laudable exercise, but the exercise could be hindered by the inevitable adjustment between pest reductions, operation costs as well as impacts on the environment and human health. The pest could be controlled by many methods, but biological control was the most popular technique because it addressed inevitable trade-offs between costs and side effects. In this paper, a mathematical model was developed to quantify intricate biological procedures in the context of biological control using prey-predator mechanisms. Three equilibrium points (one trivial and two non-trivial) were derived, and the stability of each equilibrium point was examined. The stability results indicated that the adoption of biological control might neutralize pest infestation but the situation might not persist (unstable trivial equilibrium). It was also discovered that pest control through biological means might fail if the predator was wrongly selected or if the population of the predator vanished while the pest remained in existence (unstable non-trivial equilibrium). The analytical results were finally justified by a means of simulation via a computer-in-built maple program.