考虑污染和种内关系的种群扩散最优控制模型  

Optimal Control Model of Population Diffusion System Affected by Pollution and Intraspecific Relationship

作　　者：杨露 高伟 YANG Lu;GAO Wei(Department of Statistics,Xi’an University of Finance and Economics,Xi’an 710100,China)

机构地区：[1]西安财经大学统计学院,陕西西安710100

出　　处：《运筹与管理》2023年第1期54-59,78,共7页Operations Research and Management Science

基　　金：陕西省自然科学基金项目(2022JQ-042);全国统计科学研究重点项目(2021LZ28);西安财经大学青年英才发展支持计划;西安财经大学雁塔学者支持项目;国家社会科学基金项目(20CTJ008)。

摘　　要：针对污染和种内关系均影响细菌种群扩散这一管理生态学问题,本文建立了基于非线性拟抛物方程的最优控制模型,将外界环境向细菌种群输入的毒素率作为控制变量,运用控制理论和方法探讨污染和种内关系双重影响下种群扩散系统的最优控制问题。利用Schauder不动点定理证明了该种群扩散系统的适定性;同时,通过建立新的Carleman型估计,给出了容许控制和最优控制的存在性。最后,通过数值算例分析了理论推导的结果,在算例中都找到一对时间最优控制,验证了种群扩散系统最优控制模型的有效性。该研究结果对现代传染病预防具有借鉴意义,也为有效控制瘟疫的爆发和流行提供理论参考。In order to solve the problem in management ecology that both pollution and inter-individual interactions(intraspecific relationships) seriously restrict the diffusion of bacteria population, an optimal control model based on nonlinear quasi-parabolic equation is established in this paper, in which the toxin rate imported into the population by the outside environment is regarded as the control variable. Meanwhile, the optimal control problem of population diffusion system under the influence of pollution and intraspecific relations is studied by using the control theory and method. The well-posedness of the population diffusion system is proved by the Schauder Fixed-point Theorem, and the existence of the admissible control and the optimal control is obtained by establishing a new Carleman-type estimate. Finally, a numerical example is given to analyze the results of theoretical derivation, and a pair of time optimal control is found in various cases, which verifies the effectiveness of the optimal control model of population diffusion system. The results can be used for reference in the prevention of modern infectious diseases and provide theoretical reference for the effective control of the outbreak and epidemic of plague.

关 键 词：种群扩散系统 最优控制 适定性 Carleman型估计 

分 类 号：O231.1[理学—运筹学与控制论]