This study proposes and explores a prey–predator model that presents a functional response to group behavior of prey–predator harvesting. We study a non-linear model of prey–predator growths in two species. The proposed model is supported by theoretical and numerical results. Some numerical descriptions are provided to help our analytical and theoretical conclusions. For all possible parameter values occurring in a prey–predator system, we solved it by using both VIM (variational iteration method) and HPM (homotopy perturbation method). We also used MATLAB coding to compare our approximate analytical expressions with numerical simulations. We have found that there is no significant difference when comparing analytical and numerical results.

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