Predator-prey model with constant rate of harvesting

Abstract

Predator-prey model is the first model to illustrate the interaction between predators and prey. It is a topic of great interest for many ecologists and mathematicians. This model assumes that the predator populations have negative effects on the prey populations. The generalized equation of this model is the response of the populations would be proportional to the product of their population densities. Prey population grows with limited by carrying capacity, K and it is called the logistic equation. Thus, in this research, there are four different cases are analyzed which are predator-prey model, predator-prey model with harvesting in prey, predator-prey model with harvesting in predator and predator-prey model with harvesting in both populations. Systems of ordinary differential equation are used for all models. The objectives of this research are i) to study the concept of Lotka-Volterra predator-prey model, ii) to analyze the predator-prey model with constant rate of harvesting in prey, iii) to analyze the predator-prey model with constant rate of harvesting in predator, iv) to analyze the predator-prey model with constant rate of harvesting in both populations. In analyzing all four models, equilibrium points will be obtained and analyzed for the stability by using Routh-Hurwitz Criteria. Lastly, some numerical examples and graphical analysis are shown to illustrate the stability of the stable equilibrium points and the effects of harvesting to the systems.