Numerical analysis and stability of a prey-predator model with partial refuge and continuous harvesting

Abstract

A modified prey–predator model with partial refuge and proportional harvesting is investigated. The model consists of a pair of nonlinear ordinary differential equations that describe the interaction between prey and predator. The growth of the prey population is influenced describing by logistic factors and a Holling type II response. The solution is proven to exist, be positive, and be bounded. We determine all biologically feasible equilibrium points and study their local stability using the Routh-Hurwitz. For the global stability of the boundary and interior equilibrium points, the Lyapunov function construction is also used. The analytical results are validated in the numerical simulations describing the dynamical behaviour of the system.