Impact of prey herd behavior and predator hunting cooperation on eco-epidemic dynamics with impulsive harvesting control: a real-data approach

This article studies a Holling type II eco-epidemic model exploring cooperative hunting by predators, herd behavior of susceptible prey, and refuge of disease-infected prey. The local sensitivity of R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0$$\end{document} and the global sensitivity of the system parameters on the infected prey are analyzed. Transcritical bifurcation with stability switching between the disease-predator-free equilibrium and the interior equilibrium points has been demonstrated as the disease transmission parameter changes. The direction and stability of Hopf bifurcation are also analyzed, which indicates the occurrence of a supercritical Hopf bifurcation, confirming the presence of a stable limit cycle and sustained oscillation in the system. Chaotic behavior of the system is confirmed by plotting the maximum Lyapunov exponent (MLE) as well as by showing the divergence of the solution trajectories due to sensitivity to initial conditions. Here, the period-doubling route to chaos is also observed as the conversion coefficient of susceptible prey increases. Despite the presence of chaotic dynamics, the high value of refuge, predator's handling time for susceptible prey, and low value of hunting cooperation for susceptible prey play significant roles in controlling chaos within the system. Furthermore, after introducing the harvesting process, we discretize the system and implement impulsive control to optimize harvesting effort. Real data are used for model fitting, demonstrating a strong fit as measured by the R-squared value, thereby validating the reliability of the proposed model in capturing the observed trends.