MODELING BIOLOGICAL CONTROL OF ALGAL BLOOM IN A LAKE CAUSED BY DISCHARGE OF NUTRIENTS

Abstract

This paper proposes and analyzes a nonlinear model for the biological control of algal bloom in a lake. Algal bloom often occurs in a lake due to excessive flow of nutrients from domestic drainage, industrial and agricultural waste, and this causes the decrease in the concentration of dissolved oxygen in the lake. Hence, it threatens the survival of other species of the ecosystem indirectly, and it is also responsible for the degradation of water quality in the lake because of less oxygen content. In this work we study biological control which means the introduction of predatory fish, i.e. the release of algae-eating fish into the lake to control the rapid growth of algae. We formulate our model by assuming Michaelis-Menten type ratio-dependent prey-predator interaction. The equilibrium of the mathematical model is found and also the stability is discussed in detail. It is observed that the positive equilibria is locally asymptotically stable under certain conditions on the parameters. Also the system is simulated for various sets of parameters and it is found that system may oscillate for some realistic set of parameters. In fact we found that the parameter m, which is the half saturation constant, is very sensitive and with the decrease in this parameter steady state solution of the system changes to stable oscillation. On the practical side, it means that the method of biological control by introducing predatory fish is not always beneficial because outcome of this method depends upon the actual value of the parameter. Here we get the paradox of biological control, which says that it is not possible to have low level of steady state equilibrium of prey population.