NUMERICAL ANALYSIS OF A PREDATOR–PREY MODEL WITH STAGE STRUCTURE AND SENSITIVITY INVESTIGATION

Abstract

In this paper, we analyze a stage-structured predator-prey model with juvenile and adult classes of both prey and predator populations. The model is formulated as a system of nonlinear ordinary differential equations describing biological processes such as growth, maturation, predation and natural death. The long-term dynamics of the populations is studied by obtaining the equilibrium points of the system and studying their stability. We obtain the basic reproduction number  by the next generation matrix method as a threshold parameter for persistence in population. The sensitivity analysis of  is performed to study the impact of the key parameters. The results show that the prey growth rate has a significant positive effect on  and the predation rate has a significant negative effect. Moreover, the numerical simulations are conducted by using Runge-Kutta fourth order (RK_4) method to verify the analytical results. The simulations show the time evolution of all the population classes and confirm the theoretical results about the stability and the behavior of the system. The study discusses the most important parameters governing the dynamics of the predator–prey system.