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An analysis approach to permanence of a delay differential equations model of microorganism flocculation

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    * Corresponding author 

This work is supported in part by the National Natural Science Foundation of China (Nos. 11901027, 11871093 and 11971055), the Scientific Research Project of Beijing Municipal Education Commission (No. KM201910016001), the Pyramid Talent Training Project of BUCEA (JDYC20200327) and the Bill & Melinda Gates Foundation (INV-005834)

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  • In this paper, we develop a delay differential equations model of microorganism flocculation with general monotonic functional responses, and then study the permanence of this model, which can ensure the sustainability of the collection of microorganisms. For a general differential system, the existence of a positive equilibrium can be obtained with the help of the persistence theory, whereas we give the existence conditions of a positive equilibrium by using the implicit function theorem. Then to obtain an explicit formula for the ultimate lower bound of microorganism concentration, we propose a general analysis method, which is different from the traditional approaches in persistence theory and also extends the analysis techniques of existing related works.

    Mathematics Subject Classification: Primary: 34K09, 34K25, 70K42; Secondary: 74G55.


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