Sustainable use of prey species in a prey–predator system: Jointly determined ecological thresholds and economic trade-offs

This paper deals with a prey–predator system in the presence of some alternative food to predator and harvesting of prey species. Instead of the usual harvesting function based on catch-per-unit-effort (CPUE) hypothesis, we have considered an alternative functional form to overcome some of the unrealistic features of the earlier function. In absence of exploitation, it is observed that alternative source of food to the predator has a negative effect on the growth of the prey species. Moreover, in the presence of alternative food maximum sustainable yield (MSY) level of prey exploitation may not prevent the extinction of the predator species. Hence, to protect the predator species from extinction a control instrument, tax is imposed on the landed fish and the fishing effort is taken as dynamic variable. Optimal tax policy is obtained using Pontryagin's maximum principle. Some numerical simulations are given to verify some of our analytical results and optimal and suboptimal paths are obtained.