GIORGIO BUSONI and LAURA PRATI
On mortality in a two-sex population
Received: 30 October 2008
Accepted in revised form: 8 September 2009
Mathematics Subject Classification (2000): 92D25 - 35R30
Keywords: Population dynamics, Partial differential equations with delay, Coefficient of mortality, Inverse problem.
Work partially supported by the Italian PRIN 2006 ''Kinetic and hydrodynamic equations of complex collisional systems'', and by PRSA 2007 of the University of Florence, under the auspices of GNFM-INdAM.
Abstract In this paper we consider the mathematical model of the dynamics of a two-sex population with gestation period presented by Busoni and Palczewski [Dynamics of a two sex population with gestation period, Appl. Math. (Warsaw) 27 (2000), 21-34]. We solve a system of two differential equations with delay coupled by boundary conditions to obtain the densities of males and nonpregnant females. Then, we invert the problem to obtain the male mortality coefficient, assuming the density and the mortality coefficient of females known; we possibly get a unique solution. We also look for the female mortality coefficient, assuming the density and the mortality coefficient of males known. We use the method of successive approximations which leads to the uniqueness of the solution if it converges.