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

Abstract

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.