@article{Meng2024, 
author = {Zhaoyan Meng and Shuting Lyu and Mengqing Zhang and Xining Li and Qimin Zhang},
title = {Sufficient and necessary conditions of near-optimal controls for a stochastic listeriosis model with spatial diffusion},
year = {2024},
journal = {Electronic Research Archive},
volume = {32},
number = {5},
pages = {3059-3091},
keywords = {listeriosis model, near-optimal controls, sufficient and necessary conditions, spatial diffusion},
url = {https://www.sciopen.com/article/10.3934/era.2024140},
doi = {10.3934/era.2024140},
abstract = {Random environment and human activities have important effects on the survival of listeria. In this paper, treating infected people and removing bacteria from the environment as control strategies, we developed a listeriosis model that considers random noise and spatial diffusion. By constructing a Lyapunov function, we demonstrated the existence and uniqueness of the global positive solution of the model. However, it was a challenging task to realize the optimal control of the model by solving the Pontryagin random maximum principle with the lowest control cost. Therefore, our study on near-optimal controls is of great significance for controlling the spread of listeriosis. Initially, we gave some adjoint equations and a priori estimates. Subsequently, the Pontryagin random maximum principle was utilized to establish the sufficient and necessary conditions for achieving near-optimal controls. Ultimately, the theoretical findings are corroborated through numerical analysis.}
}