Preprint Incorporating prey refuge in a predator-prey system with imprecise parameter estimates Qinglong Wang a, * , Zhijun Liu b, † , Xingan Zhang a, ‡ , Robert A. Cheke c, § a School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, P.R.China b Department of Mathematics, Hubei University for Nationalities, Hubei 445000, P.R.China c Natural Resources Institute, University of Greenwich at Medway, Central Avenue Chatham Maritime, Chatham, Kent ME4 4TB, UK Abstract: This article concerns with the optimal harvesting of a predator-prey model with prey refuge and imprecise biological parameters. We consider the above model under impreciseness and introduce parametric functional form of an interval which are different from that of models with precise biological parameters. We study the existence and stability of the equilibria. The bionomic equilibria of the model are discussed. Also, the optimal harvesting policy is derived by using Pontryagin’s maximal principle. Numerical simulations are presented to verify the feasibility of our analytical results. Keywords: Predator-prey system; refuge; interval number; equilibrium; stability; optimal harvesting policy. * E-mail: wangqinglong125@163.com (Q.Wang) † Corresponding author. E-mail: zhijun liu47@hotmail.com (Z.Liu). Tel/Fax: +86(0)7188437732. ‡ E-mail: zhangxinan@hotmail.com (X.Zhang) § E-mail: r.a.cheke@greenwich.ac.uk (R.A. Cheke) 1 The final publication is available at Springer via http://dx.doi.org/10.1007/s40314-015-0282-8