Mathematical modelling of ecosystem sustainability in the presence of nutrient, consumers and predator food web

A nonlinear mathematical model is formulated and analysed to study the ecosystem sustainability in the presence of nutrient, consumers and predator food web. In modelling the dynamics of the system, the population is divided into three interacting species namely nutrient, consumers and predators. The model is analysed qualitatively to determine the boundedness and positivity of solutions. Positivity of the system has revealed that all state variables are nonnegative for all 0. t The existence and stability of the equilibrium points are qualitatively analysed. It is established that the system has four equilibrium points namely: the trivial equilibrium point, the axial equilibrium point, the predator-free equilibrium point and the interior equilibrium point. The local stability of equilibrium points for nutrient, consumers and predators are analysed using Jacobian matrix method and it is found out that the trivial equilibrium point is locally asymptotically stable and the axial equilibrium point is locally asymptotically stable and unstable otherwise. The predator-free equilibrium point is found to be locally asymptotically stable. The interior equilibrium point is analysed using Routh-Hurwitz criteria and the steady state is found to be locally asymptotically stable. Furthermore, numerical simulations of the model are carried out showing the effects of predator dependence on both nutrient and consumers. Finally, it is concluded from the study that through the predator dependence on both nutrient and consumers, the increase of nutrient and consumers lead to the increase of predator population.