Optimal Control for Stochastic SIR model of Dengue with Brownian Motion

In this study, we develop a model for dengue that incorporates spatial diffusion and Brownian motion to explore the stationary distribution and optimal control strategies for a stochastic dengue model. We begin by demonstrating the existence of a globally positive solution by constructing a Lyapunov function. We then determine sufficient conditions under which a stationary distribution exists and is unique for this positive solution. Following this, we implement control strategies to reduce the number of infected individuals and apply mosquito insecticides. By utilizing Pontryagin's maximum principle and the Euler-Maruyama method, we implement control strategies to reduce the number of infected individuals and apply mosquito insecticides. Finally, we conduct numerical simulations to validate our analytical findings. The simulations confirm the presence of a stationary distribution and reveal variations in the stationary distribution solutions across different spatial domains. Additionally, we examine the impact of varying noise intensities on the stationary distribution and assess the effectiveness of various control strategies for managing stochastic dengue fever.