Fuzzy Logic Theory and Spatiotemporal Modeling of the Fungus Phakopsora pachyrhizi Based on Differential Equations

Brazil has been one of the largest soybean producers in recent years. The soybean is a legume commonly found in family meals. Among the diseases affecting the grains, Asian soybean rust is one of the most concerning. The fungus causing the disease is spread by the wind, making it difficult to control. Although it has been researched since its first records, not much data are available regarding the macro propagation behavior of spores. Therefore, this research aimed to model its dispersion based on a partial differential equation, the diffusion–advection equation, used by researchers to model the behavior of any pollutant. The terms of this equation were developed from real data, processed by fuzzy logic, and the simulation results were compared with disease records throughout a harvest. By using this approach to model the spatiotemporal dynamics of this fungus, it was possible to simulate its spread satisfactorily. Additionally, its results were used as input variables for a fuzzy system that estimates the susceptibility of a given location to disease development.