Role of Age-selective Harvesting in a Delayed Predator- prey Model together with Fear and Additional Food

In this paper, we have discussed the dynamical behaviour of a delayed induced harvested predator-prey model incorporating both effects of fear (felt by prey) and additional food (provided to the predator). Hence we have considered selective harvesting terms in both the species that provides some fixed elapsed time to prey and predator population before they are harvested. Ecologically, harvesting of population are restrained below certain age to protect juvenile population. Also the reproduction of prey population can be greatly hindered due to the influence of fear effect. However, to increase the growth rate of predator and to decrease the predatory attack rate on the prey population, it is necessary to incorporate additional food to the predator for maintaining ecological balance. Consideration of age-selective harvesting together with fear effect and additional food compel the proposed system to exhibit Hopf-bifurcation around the coexistence equilibrium point. For better ecological community management, our study reveals the fact that harvesting delay and harvesting intensities should be maintained. Numerical simulations have been performed to validate the analytical findings.