Decoding Yellow Virus Dynamics in Chili Crops: A Stochastic Approach Using Neural Networks

Cultivating red chili or Capsicum annuum is important in agriculture in terms of the economy and food. However, the disease known as the yellow virus, which is transmitted through a vector, has caused enormous losses in crops, requiring new advanced predictive models for the control of new diseases. Most of these conventional numerical methods could not effectively capture the non-linear dynamics of disease transmission; therefore, more research is needed on computational approaches. This optimization study aims to create a stochastic modeling framework with Levenberg-Marquardt backpropagation neural networks (LMB) to improve the precision of the prediction of the spread of the yellow virus in chili crops. The new model of the LMB neural network was trained and validated against numerical solutions using the Adam solver. The model minimizes the mean square error (MSE) to be <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mn>1.54</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>11</mml:mn> </mml:mrow> </mml:msup> </mml:math> to mark its highly accurate predictability. Shows a regression analysis of a correlation coefficient <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>R</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>0.99</mml:mn> </mml:math> , which confirms it to be a reliable prediction. In addition, stability analysis according to the basic reproduction number <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:msub> <mml:mi>R</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> is performed to evaluate the dynamics of disease spread. It is proven that the bona fide LMB neural network surpasses numerical methods or traditional solvers in efficiency in computation and accuracy and hence can be considered a precious asset in real-time forecasting of crops or plant diseases. It also demonstrates a bright future for neural networks in plant disease modeling. It can practically move into data-driven precision agriculture, optimize pest control measures, and promote sustainable crop management strategies.