A stage-structure predator-prey model with ratio-dependent functional response and anti-predator

This article discusses a stage-structure predator-prey model with ratio-dependent functional response. The proposed mathematical model is a system of three nonlinear ordinary differential equations that describes the interactions between prey population, juvenile predator, and adult predator. It is assumed that only adult predators attack and consume the prey and have the ability to reproduce. Here, we also consider an anti-predator defense effects where prey can attack juvenile predator. However, it is also assumed that adult predators may help when juvenile predators are attacked by prey. The proposed model is analyzed dynamically, which includes the existence and local stability of equilibrium points. There are two equilibria, namely the predator extinction point and the co-existence point. The predator extinction point is always there but it is conditionally stable. If there exists a co-existence point, then this point is also conditionally stable. Numerical solutions are carried out to illustrate the theoretical results.