Logistic Growth Model of Field Crops with Pest Control Measures

In this paper a logistic growth model of field crops is formulated and analysed to examine the best measure to reduce pest infestation to enhance food security. A control model is developed based on three control measures; the prevention measure (u1) that protect susceptible crops from pest (the rate of brush trimming and removal of weeds), pesticide control measure (u2) and the rate of removal of infected plants (u3). The effective reproduction number that determines pest extinction and crop survival is obtained and use to establish the condition for the local asymptotic stability of the pest-free equilibrium using the method of linearization. The existence of the pest- endemic equilibrium is verified using the Descartes rule of signs. Numerical simulations are performed to reveal the effects of the control measures on the field crops. The findings show that each integrated measure is able to mitigate pest infestation in the specified time.