Allee effect

Stability (learning theory)

Physics

Sociology

Nonlinear system

Bifurcation

Population

Mathematics

Biology

Functional response

Machine learning

Demography

Limit (mathematics)

Mathematical analysis

Artificial intelligence

Predation

Hopf bifurcation

Control (management)

Ecology

Comparison theorem

Computer science

Quantum mechanics

Differential equation

Applied mathematics

Equilibrium point

Predator

Control theory (sociology)

Lyapunov function

Limit cycle

International Journal of Bifurcation and Chaos

Here, we have proposed a predator–prey model with Michaelis–Menten functional response and divided the prey population in two subpopulations: susceptible and infected prey. Refuge has been incorporated in infected preys, i.e. not the whole but only a fraction of the infected is available to the predator for consumption. Moreover, multiplicative Allee effect has been introduced only in susceptible population to make our model more realistic to environment. Boundedness and positivity have been checked to ensure that the eco-epidemiological model is well-behaved. Stability has been analyzed for all the equilibrium points. Routh–Hurwitz criterion provides the conditions for local stability while on the other hand, Bendixson–Dulac theorem and Lyapunov LaSalle theorem guarantee the global stability of the equilibrium points. Also, the analytical results have been verified numerically by using MATLAB. We have obtained the conditions for the existence of limit cycle in the system through Hopf Bifurcation theorem making the refuge parameter as the bifurcating parameter. In addition, the existence of transcritical bifurcations and saddle-node bifurcation have also been observed by making different parameters as bifurcating parameters around the critical points.

A Michaelis–Menten Predator–Prey Model with Strong Allee Effect and Disease in Prey Incorporating Prey Refuge