Mathematical model for soybean mosaic disease transmission with entomopathogen interventions and photoperiodicity

Abstract

Mosaic is a severe disease of soybeans that has the potential to reduce the quality and quantity of soybean production. The Mosaic disease can infect soybean plants by the Aphis vector carrying Soybean Mosaic Virus (SMV). In this study, a mathematical model of the spread of Mosaic disease was built by considering two interventions, namely the application of entomopathogen and the regulation of photosynthesis intensity. This research focuses on knowing the effect of intervention in controlling Mosaic disease and increasing the population of susceptible generative plants. Using dynamical system theory, non-endemic and endemic equilibrium points and their stability are obtained. Then, the basic reproduction ratio (R₀) is obtained for this model. Sensitivity analysis was carried out to determine the most influential parameters in the model. Optimal control theory was used to determine the optimal conditions of the model by considering the cost of entomopathogen application and photoperiodicity. The results of numerical simulations show that the application of entomopathogen and photosynthetic intensity can suppress the population of plant and vector infections and increase the population of susceptible plants in the generative phase at the same time.