Effect of Fear, Treatment, and Hunting Cooperation on an Eco-Epidemiological Model: Memory Effect in Terms of Fractional Derivative

In this paper, we have studied a fractional-order eco-epidemiological model incorporating fear, treatment, and hunting cooperation effects to explore the memory effect in the ecological system through Caputo-type fractional-order derivative. We have studied the behavior of different equilibrium points with the memory effect. The proposed system undergoes through Hopf bifurcation with respect to the memory parameter as the bifurcation parameter. We perform numerical simulations for different values of the memory parameter and some of model parameters. In the numerical results, it appears that the system is exhibiting a stable behavior from a period or chaotic nature with the increase in the memory effect. The system also exhibits two transcritical bifurcations with respect to the growth rate of the prey. At low values of prey's growth, all species go to extinction, at moderate values of prey's growth, only preys (susceptible and infected) can survive, and at higher values of prey's growth, all species survive simultaneously. The paper ended with some recommendations.

Automated summary

This paper investigates the impact of memory effect on the behavior of an eco-epidemiological model in an ecological system by incorporating Caputo-type fractional-order derivative. The study reveals that the system exhibits stable, periodic, or chaotic behavior with increasing memory effect, and different equilibrium points are observed. The numerical simulations demonstrate that the growth rate of the prey plays a significant role in determining the survival or extinction of the species.