• 关键词：数学模型  半抑制浓度(EC₅₀)  最小有效浓度(MIC)  成本控制  最佳组合

• 基金项目：国家自然科学基金项目(No.30870429); 安徽师范大学创新基金项目(No.2011cxjj05)

• 何宗祥
• 安徽师范大学数学计算机科学学院, 芜湖 241000

• 张庭廷
• 安徽师范大学生命科学学院, 芜湖 241000

• 摘要：在化感物质焦性没食子酸和亚麻酸单独抑藻的基础上,将两种化感物质按不同初始浓度组合进行联合抑藻的实验.根据实验过程中藻密度的变化趋势及特征,采用微元分析法,通过相应的偏微分方程,建立了化感物质复合抑藻时的数学模型.结果表明,该模型能够有效地分析和预测焦性没食子酸与亚麻酸在一定浓度范围内联合抑藻时藻密度随时间的变化规律.根据该模型还可以预测不同时间节点上,化感物质复合抑藻的半抑制浓度(EC₅₀)、最小有效浓度(MIC),以及联合抑藻的最佳浓度组合和在成本控制下的联合抑藻最佳浓度组合等.该研究对指导制备高效、经济的复合生物抑藻剂及其应用均具有一定的理论意义和实用价值.

• Abstract：Based on the separate algal inhibition effects of two allelochemicals, pyrogallic and linolenic acid, the joint algal growth inhibition effects of varying combinations of these two allelochemicals were studied. The mathematical model of algal growth inhibition by combined effects of the two allelochemicals was established by micro-element analysis and relevant partial differential equation, based on the dynamics and characteristics of algal density during experiment. The law of algal density changing with time can be effectively analysed and forecast by this model when joint pyrogallic and linolenic acid in certain concentration range used to inhibit algal growth. Based on this model, the half effective concentration (EC₅₀) and the minimal inhibitory concentration (MIC) of combined algal growth inhibition effect of allelochemicals, the optimal combination of concentration for joint algal growth inhibition, as well as the optimal combination of concentration for joint algal growth inhibition in the context of cost control at different time points can be projected. The finding of the present study was of theoretical significance and practical value for guiding the preparation of efficient and economical joint biological algal growth inhibitory agents.

• Key words：mathematical model  half maximal effective concentration (EC₅₀)  minimal inhibitory concentration (MIC)  cost control  the best combination

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