**GIORGIO BUSONI** and **LAURA PRATI**

*On mortality in a two-sex population*

**Pages** 19-54

**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.

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