A growth rate control problem of harmful species population and its application to algae bloom

  • Hidekazu YoshiokaEmail author
  • Yuta Yaegashi


A mathematical framework for controlling growth rate of harmful species population is established based on the concept of stochastic control. The main problem to be addressed in this paper is to effectively suppress the population growth through manipulating its surrounding environmental conditions. The growth control is achieved through minimization of a performance index that contains the cost of interventions and a metric based on the growth rate. Solving the problem ultimately reduces to finding a solution to the associated Hamilton–Jacobi–Bellman equation. Its solution behavior is analyzed from a mathematical viewpoint, showing that the optimal control and the optimized growth rate are critically affected by the chosen metrics in the performance index. The present model is then applied to an urgent management problem of the harmful attached algae in a dam downstream river reach, in which the dam discharge is the control variable. The application results clarify environmental dependence of the optimal dam discharge and under what condition it serves as the environmental flow to suppress the algae bloom. Throughout this paper, we demonstrate how mathematical models can be applied to environmental decision-making.


Population dynamics Stochastic control Hamilton–Jacobi–Bellman equation Attached algae 



We acknowledge the support through JSPS Research Grant Nos. 17K15345 and 17J09125 for this research.


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Authors and Affiliations

  1. 1.Faculty of Life and Environmental ScienceShimane UniversityMatsueJapan
  2. 2.Graduate School of AgricultureKyoto UniversityKyotoJapan
  3. 3.Japan Society for the Promotion of ScienceTokyoJapan

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