Mathematical modelling and analysis of fish population dynamics in acidified lakes with liming activities

Acidic rain is a great threat in the world. It kills the fish and other aquatic species in our lakes. In this study, a mathematical model is developed to study the analysis of the fish population dynamics by taking into account the effects of acidic chemicals on the fish population and the effects of application of liming on it. Also the model is developed by incorporating the Holling type II harvest term as the control parameter of the fishing activities. Using stability theory of Ordinary Differential Equations (ODE), the four non trivial equilibria are determined in which equilibrium point 0E is locally asymptotically stable, 1E is locally unstable, 2E is locally asymptotically stable whereas the equilibrium point 3E is globally unstable.From numerical simulation (Computer simulation through Matlab program) of the model, it is shown that due to application of liming (effort) in the acidified lakes, the amount of acid chemicals is reduced to a permisible level to restore our fish population and other aquatic species from extinction. Moreover, the Holling type II harvest term in the model limits the number of fish harvesting to half its value.