Dynamics of Powdery Mildew Transmission in Cashew Plants Under Lévy Noise: A Nonlinear Stochastic Model

Powdery Mildew is a global plant disease caused by fungal species, causing powdery growth on various parts of plants. This study aims to develop, evaluate and simulate the transmission dynamics of Powdery Mildew in cashew plants using a stochastic differential equation with Lévy noise. After providing some preliminary definitions of stochastic differential equations, we first consider the model without noise. We prove positivity, compute the basic reproduction number, R0, the PMD-free equilibrium, and the existence of a unique endemic equilibrium point whenever R0>1. After that, we formulate the stochastic model under Lévy noise. For this model, we also prove the positivity of the solutions and show that it is possible to extend the disease when Ss<1. We also found the condition that ensures the persistence of the disease if S0s>1. To simulate the model, we build a stochastic model numerical scheme and do a number of numerical simulations to support the theoretical findings we have gotten.