基于鞘氨醇单胞菌降解微囊藻毒素的微分方程模型与理论分析  

Differential Equation Model Describing Degradation of Microcystins(MCs)and Its Theoretical Analysis

作　　者：杨凯莉 马万彪[1] 江志超 闫海[3] YANG Kai-li;MA Wan-biao;JIANG Zhi-chao;YAN Hai(School of Mathematics and Physics,University of Science and Technology Beijing,Beijing 100083,China;Fundamental Science Department,North China Institute of Aerospace Engineering,Langfang 065000,China;School of Chemistry and Biological Engineering,University of Science and Technology Beijing,Beijing 100083,China)

机构地区：[1]北京科技大学数理学院,北京100083 [2]北华航天工业学院基础部,河北廊坊065000 [3]北京科技大学化学与生物工程学院,北京100083

出　　处：《数学的实践与认识》2021年第20期231-247,共17页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11071013,11971055)。

摘　　要：蓝藻水华暴发的预防是水环境治理中世界性难题之一,蓝藻水华污染造成的最主要危害之一是在水体中产生和释放微囊藻藻毒素为主的多种藻毒素,进而引发人类原发性肝癌.微囊藻毒素稳定的化学性质使得对其降解的研究成为高度关注的课题之一.研究发现,生物降解微囊藻毒素具有高效、成本低、无二次污染等优点.近年来,一些学者对鞘氨醇单胞菌降解微囊藻毒素进行了探索性的实验研究,并发现鞘氨醇单胞菌可以通过产生降解酶降解微囊藻毒素.利用微分方程等数学理论,建立了一类描述微囊藻毒素、鞘氨醇单胞菌和鞘氨醇单胞菌产生的降解酶三者之间相互作用的微分方程模型.然后,通过对模型的平衡点稳定性和持久性等理论分析,考虑了微囊藻毒素降解过程中的控制策略等.The prevention of the outbreak of Cyanobacteria blooms has very important significance in water environment treatment.One of the main hazards caused by the outbreak of Cyanobacteria blooms is the release of a variety of Cyanobacterial toxins in the water body.It is found that the toxin released from Microcystins can cause liver cancer in humans.The chemical structure of Microcystins are very stable.Hence,the degradation of Microcytins attracts increasing worldwide attention.In the degradation of Microcystins,the biological methods have the advantages,high efficiency,low cost,no secondary pollution and so on.In recent years,the experimental results show that Sphingomonas can produce an enzyme which has the functionals in the degradation of Microcystins.In this paper,a class of differential equation model is proposed to describing the interactions among Microcystins,Sphingomonas and degradation enzyme.Then,through theoretic analysis of the stability of the equilibria and uniform persistence of the model,the control strategy related to the degradation of Microcystins are discussed.

关 键 词：微囊藻毒素 鞘氨醇单胞菌 生物降解 微分方程模型 稳定性 持久性 

分 类 号：X172[环境科学与工程—环境科学] O175[理学—数学]