Modeling the Effects of Insects and Insecticides with External Efforts on Agricultural Crops

Abstract

In this paper, we propose a continuous dynamical model along with its discretized system to increase the agricultural crop production using some external efforts in presence of insects and insecticides. It is assumed that agricultural crops grow logistically and its growth deplete due to insect population, which is wholly dependent on crops. Farmers use insecticides to kill insects to protect the crop and its excessive use is hazardous to human health and therefore it is assumed that insecticides are used proportional to the density of insects. To increase field’s growth potential, we presumed that some efforts (e.g. seed selection, use of fertilizers, proper water drainage, etc.) are applied proportional to the difference between carrying capacity and actual production. The quantitative features of the nonlinear crop production model is examined by a coherent non-standard finite difference scheme (NSFDS) in the absence of theoretical solution values. This scheme is formulated by discretizing the model system and renormalizing the denominator of derivatives of continuous system. Convergence analysis of the new NSFD scheme is described in detail. A graphical layout by computer-assisted numerical results is introduced to observe the effects of external efforts on production of agricultural crops.