Trends in Applied Sciences Research1819-35792151-7908Academic Journals Inc.10.3923/tasr.2007.271.283T.K. KarH. Matsuda4200724Traditional models of population growth assume that reducing the density will always result in the same or higher per-capita growth. This implies that populations are resilient, allowing them to recover rapidly when the factors that caused their decline are removed (e.g., fishing). However some populations experience reduced rates of survival and reproduction when reduced to very low densities. This reduced per-capita growth rate at low densities is called depensation. In this study we have considered a prey-predator model with strong Allee effect. We obtain the conditions for the existence of biological equilibrium and its stability is discussed. We have also discussed the bifurcation analysis of the model under different scenario. The bioeconomic models herein proposed, based on optimal control theory, can form a basis for more sustainable management. Mathematics Subject Classifications (2000): 34K20, 37G15, 49J15]]>Berck, P.,1981Butterworth, D.S., K.L. Cochrane and J.A.A.D. Oliveira,1997Clark, C.W.,1990Courchamp, F., T.C. Brock and B. Grenfell,1999Hassard, B.D., N.D. Kazarinoff and Y.H. Wan,1981Kent, A., P. Doncaster and T. Sluckin,2003Lande, R., S. Engen and B.E. Saether,1994Liermann, M. and R. Hilborn,2001Matsuda, H. and P. Abrams,2006Mullon, C., P. Freon and P. Cury,2005Pontryagin, L.S., V.G. Boltyansk, K.V. Gamkrelidre and E.F. Mishchenko,1964Rosser, J.B.Jr.,2002