Modelling Effects of Eutrophication on the Survival of Fish Population Incorporating Nutrient Recycling

Abstract

It is well known that the aquatic bodies undergo eutrophication process due to the nutrient enrichment caused by waste disposal from
industries and discharge of chemicals from the agricultural fields consequently, increasing the concentration of phytoplankton and algae thereby decreasing the dissolved oxygen and transparency of the aquatic environment. Due to oxygen deficit and loss of transparency, growth of much aquatic population such as fish is adversely affected. In view of this, therefore, in this paper mathematical models are proposed to study the survival or extinction of fish populations incorporating the impact of direct and indirect recycling of the nutrients under the adverse effects of eutrophication .The mathematical models have been formulated in the
form of system of non-linear partial differential equations by taking the phenomenon of diffusion (dispersal) into account. Models have been analysed by obtaining the criteria for local stability and global stability of three feasible equilibrium points. It is found that the two positive equilibrium states which are unstable without diffusion may become stable by introducing diffusion. On the basis of this analysis, conditions for the survival or extinction of the fish populations have been derived.