Sufficient and necessary conditions of near-optimal controls for a stochastic listeriosis model with spatial diffusion

Zhaoyan Meng; Shuting Lyu; Mengqing Zhang; Xining Li; Qimin Zhang; Zhaoyan Meng; Shuting Lyu; Mengqing Zhang; Xining Li; Qimin Zhang

doi:10.3934/era.2024140

Electronic Research Archive

2024, Volume 32, Issue 5: 3059-3091. doi: 10.3934/era.2024140

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Research article

Sufficient and necessary conditions of near-optimal controls for a stochastic listeriosis model with spatial diffusion

1.
School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China
2.
School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China

Received: 26 November 2023 Revised: 28 March 2024 Accepted: 16 April 2024 Published: 23 April 2024

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.
- listeriosis model,
- near-optimal controls,
- sufficient and necessary conditions,
- spatial diffusion
Citation: Zhaoyan Meng, Shuting Lyu, Mengqing Zhang, Xining Li, Qimin Zhang. Sufficient and necessary conditions of near-optimal controls for a stochastic listeriosis model with spatial diffusion[J]. Electronic Research Archive, 2024, 32(5): 3059-3091. doi: 10.3934/era.2024140

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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.

References

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