DYNAMIC ANALYSIS AND OPTIMAL CONTROL OF A TOXICANT-POPULATION MODEL WITH REACTION-DIFFUSION

An Ma; Jing Hu; Qimin Zhang

doi:10.11948/20210438

2024 Volume 14 Issue 2

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An Ma, Jing Hu, Qimin Zhang. DYNAMIC ANALYSIS AND OPTIMAL CONTROL OF A TOXICANT-POPULATION MODEL WITH REACTION-DIFFUSION[J]. Journal of Applied Analysis & Computation, 2024, 14(2): 579-605. doi: 10.11948/20210438

Citation:

An Ma, Jing Hu, Qimin Zhang. DYNAMIC ANALYSIS AND OPTIMAL CONTROL OF A TOXICANT-POPULATION MODEL WITH REACTION-DIFFUSION[J]. Journal of Applied Analysis & Computation, 2024, 14(2): 579-605. doi: 10.11948/20210438

DYNAMIC ANALYSIS AND OPTIMAL CONTROL OF A TOXICANT-POPULATION MODEL WITH REACTION-DIFFUSION

1.
School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China

Author Bio: Email: maan23@sina.com(A. Ma)
Corresponding authors: Email: hujing2002@hotmail.com(J. Hu); Email: zhangqimin64@sina.com(Q. Zhang)
Fund Project: The authors were supported by National Natural Science Foundation of China (Nos. 12161068, 12301630, 12261069, 12272196) and National Science Foundation of Ningxia (Nos. 2023AAC03085, 2022AAC03074, 2021AAC03065)

Abstract

Abstract

In this paper, we study the threshold dynamics and optimal control of a toxicant-population model with reaction-diffusion to understand how toxicant affect populations. In order to obtain the extinction and persistent conditions of the toxicant, the basic reproduction number of the model is considered, when $ R_0<1 $, the toxicant-free equilibrium is globally attractive, when $ R_0>1 $, the solution to the system is uniformly persistent. We also introduce the optimal control strategy, with the method of dynamic programming, the Hamilton-Jacobi-Bellman (HJB) equation is constructed and the optimal control is obtained. Finally, we conduct numerical simulations to verify the theoretical analysis.
- Toxicant-population model /
- reaction-diffusion /
- basic reproduction number /
- optimal control /
- Hamilton-Jacobi-Bellman equation
MSC: 35R10, 37N35, 92D25

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References

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