• PERSISTENCE AND OPTIMAL HARVESTING OF MARINE POPULATION AFFECTED WITH PRIMARY AND SECONDARY TOXICANT

PRAGYA MISHRA, RACHANA PATHAK*, MANJU AGARWAL

Abstract


This work investigates the affect of toxicant which is structured into two stages, primary and secondary on a single species fishery model. Boundedness and positivity of solution has been shown in order to ensure feasibility of biological model. The time lag required for transmission of primary toxicant to secondary toxicant is incorporated and resulting delayed model is analyzed for stability. Optimal harvesting policy has been discussed by using Pontryagin’s Principal. Butler-Mc Gehee lemma is used to identify the condition which influences the persistence of the system. Finally, some numerical simulations are given to verify the mathematical conclusions.


Keywords


Stability, Time-delay, Optimal harvesting, Persistence.

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