### Mathematical Biosciences and Engineering

2022, Issue 11: 11260-11280. doi: 10.3934/mbe.2022525
Research article

# Stationary distribution and optimal control of a stochastic population model in a polluted environment

• Received: 15 June 2022 Revised: 16 July 2022 Accepted: 24 July 2022 Published: 05 August 2022
• This paper is concerned with a stochastic population model in a polluted environment. First, within the framework of Lyapunov method, the existence and uniqueness of a global positive solution of the model are proposed, and the sufficient conditions are established for existence of an ergodic stationary distribution of the positive solution. Second, the control strategy is introduced into the stochastic population model in a polluted environment. By using Pontryagin's maximum principle, the first-order necessary conditions are derived for the existence of optimal control. Finally, some numerical simulations are presented to illustrate the analytical results.

Citation: An Ma, Shuting Lyu, Qimin Zhang. Stationary distribution and optimal control of a stochastic population model in a polluted environment[J]. Mathematical Biosciences and Engineering, 2022, 19(11): 11260-11280. doi: 10.3934/mbe.2022525

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• This paper is concerned with a stochastic population model in a polluted environment. First, within the framework of Lyapunov method, the existence and uniqueness of a global positive solution of the model are proposed, and the sufficient conditions are established for existence of an ergodic stationary distribution of the positive solution. Second, the control strategy is introduced into the stochastic population model in a polluted environment. By using Pontryagin's maximum principle, the first-order necessary conditions are derived for the existence of optimal control. Finally, some numerical simulations are presented to illustrate the analytical results.

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沈阳化工大学材料科学与工程学院 沈阳 110142

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