MATHEMATICAL MODEL OF PREDATOR-PREY RELATIONSHIP WITH HUMAN DISTURBANCE

MATHEMATICAL MODEL OF PREDATOR-PREY RELATIONSHIP WITH HUMAN DISTURBANCE

ABSTRACT

The predator-prey model with human disturbance is considered in the model and other factors such as noise, diffusion and external periodic force. The functional response of Holling III is also involved in the study. This predator-prey model involves two species giving us two variables (the predator and prey).  The oscillatory wave in two-dimensional space is shown by the species with time which is obvious when human disturbance and noise are involved.   In this model, the coefficient of diffusion is zero at the point predator is predating on the prey. Also, the effect of the said factor (human disturbance) leads the prey to quick annihilation from the system of interaction at the beginning of the competition and later comes up in its population in an asymptotic and exponential increase respectively. The study when modeled with noise and periodic force showcased a sinusoidal and an exponential increase in the figures below; and without noise and periodic force depicted an asymptotical increase in the shape of the graph figures below.  These results may help us to understand the effects springing up from the true defenselessness to random fluctuations in the real ecosystems. We declared that the human disturbance increases the functional response and the entire processes of motion (diffusion) which showed us that the predator haspr only one type of food source.  Both the prey and predator will survive the contest. The study has showcased the rate of the predator’s functional response with time, t. We analyzed and discussed the equilibria, stability of the model and solutions of these systems of differential equations. We also used the figures to illustrate the predator-prey interaction in terms of their population which exists in an ecosystem, predator-prey life in an ecological system, a predator predating on its prey and the intensity of human disturbance in the same ecosystem. We performed simulations by illustrating the rate of the predator’s feeding on the prey with time using the Holling-Type III functional response showing the searching time, handling time and total time of the predator in predating on its prey. We used scilab in the simulations as shown in figures 1 to 15.

Keywords: predator-prey model, human disturbance, external periodic force and noise.