An ecoepidemic model with healthy prey herding and infected prey drifting away

Abstract

We introduce here a predator–prey model where the prey are affected by a disease. The prey are assumed to gather in herds, while the predators are loose and act on an individualistic basis. Therefore their hunting affects mainly the prey individuals occupying the outermost positions in the herd, which is modeled via a square root functional response. The conditions of boundedness and uniform persistence are established. Stability and bifurcation analysis of all feasible equilibrium are carried out. Conditions on the model parameters for the possible existence of limit cycles are derived, global stability analysis is also shown in proper choice of suitable Lyapunov function. Numerical simulation of the various bifurcations validate the theoretical results. It is found that the system ultimate behavior depends mainly on two crucial parameters, the force of infection and predator average handling time. A discussion of the biological significance of the investigation concludes the paper.

Keywords

• ecoepidemic model
• herd behavior
• disease in prey
• bifurcations
• limit cycle
• uniform persistence