A study on imprecise mathematical model for optimal management and utilization of renewable resource by population

Abstract

The development and survival of the biological population depend heavily on the availability of food and other materials that may be produced from renewable resources. In real life situation the information reported about the parameters of ecological model system may not be precise due to various issues like insufficient data, error in data collection, wrongly measurement etc. To address all of these challenges, an ecological model system must be developed in an ambiguous setting where the ecological parameters are handled as different kinds of fuzzy numbers. In this article, we present an imprecise mathematical model for optimal management and utilization of renewable resources by population. We introduce the model system in interval environment and apply a parametric form of interval number which makes different form of crisp ecological model. The positivity and boundedness of the proposed model system are checked. The stability criterion of feasible equilibrium points and bionomical equilibrium have been discussed. Moreover maximum sustainable strategy and optimal harvesting strategy are analyzed using interval number. Numerical discussion are provided to verify the result of the proposed system.