Stability of a fractional order harvested prey–predator model in the existence of infection in prey

Abstract

The growing relationship between prey and their predator is one of the important aspects in the field of ecology and mathematical biology. On the other hand, the utility of fractional calculus in different types of mathematical modelling have been applied extensively. In this paper, a fractional order prey–predator model is developed with the consideration of Holling type-I and Holling type-II functional response of the predator. As infection spreads through prey, the prey population is divided into two parts. In addition, we exploit the effect of harvesting to control the excessive spread of the infection. The existence and uniqueness criteria, the boundedness of the solution of the proposed model are investigated. A number of five possible equilibrium points of the proposed model are determined along with the feasibility conditions for each equilibrium points. The local stability at these equilibrium points and global stability at interior equilibrium point are investigated. Numerical simulation is presented with the help of modified Predictor-corrector method in MATLAB software to understand the dynamics of the proposed model.