Cannibalistic enemy-pest model: effect of additional food and harvesting.

Biological control using natural enemies with additional food resources is one of the most adopted and ecofriendly pest control techniques. Moreover, additional food is also provided to natural enemies to divert them from cannibalism. In the present work, using the theory of dynamical system, we discuss the dynamics of a cannibalistic predator prey model in the presence of different harvesting schemes in prey (pest) population and provision of additional food to predators (natural enemies). A detailed mathematical analysis and numerical evaluations have been presented to discuss the pest free state, coexistence of species, stability, occurrence of different bifurcations (saddle-node, transcritical, Hopf, Bogdanov-Takens) and the impact of additional food and harvesting schemes on the dynamics of the system. It has been obtained that the multiple coexisting equilibria and their stability depend on the additional food (quality and quantity) and harvesting rates. Interestingly, we also observe that the pest population density decreases immediately even when small amount of harvesting is implemented. Also the eradication of pest population (stable pest free state) could be achieved via variation in the additional food and implemented harvesting schemes. The individual effects of harvesting parameters on the pest density suggest that the linear harvesting scheme is more effective to control the pest population rather than constant and nonlinear harvesting schemes. In the context of biological control programs, the present theoretical work suggests different threshold values of implemented harvesting and appropriate choices of additional food to be supplied for pest eradication.