Most plant viral infections are vector-borne. There is a latent period of disease inside the vector after obtaining the virus from the infected plant. Thus, after interacting with an infected vector, the plant demonstrates an incubation time before becoming diseased. This paper analyzes a mathematical model for persistent vector-borne viral plant disease dynamics. The backpropagated neural network based on the Levenberg–Marquardt algorithm (NN-BLMA) is used to study approximate solutions for fluctuations in natural plant mortality and vector mortality rates. A state-of-the-art numerical technique is utilized to generate reference data for obtaining surrogate solutions for multiple cases through NN-BLMA. Curve fitting, regression analysis, error histograms, and convergence analysis are used to assess accuracy of the calculated solutions. It is evident from our simulations that NN-BLMA is accurate and reliable.

In this study, we provide a discretized system of a continuous dynamical model for enhancing crop production in the presence of insecticides and insects. Crops are assumed to grow logistically but are limited by an insect population that entirely depends on agriculture. To protect crops from insects, farmers use insecticides, and their overmuch use is harmful to human health. We assumed that external efforts are proportional to the gap between actual production and carrying capacity to increase the field’s development potential. We use the Levenberg–Marquardt algorithm (LMA) based on artificial neural networks (NNs) to investigate the approximate solutions for different insecticide spraying rates. “NDSolve” tool in Mathematica generated a data collection for supervised LMA. The NN-LMA approximation’s value is achieved by the training, validation, and testing reference data sets. Regression, error histograms, and complexity analysis help to validate the technique’s robustness and accuracy.