Identifiability problem for recovering the mortality rate in an age-structured population dynamics model

Antoine Perasso (1) , Ulrich Razafison (2)

1 LCE - Laboratoire Chrono-environnement (UMR 6249)
2 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)

In this article is studied the identifiability of the age-dependent mortality rate of the Von Foerster-Mc Kendrick model, from the observation of a given age group of the population. In the case where there is no renewal for the population, translated by an additional homogeneous boundary condition to the Von Foerster equation, we give a necessary and sufficient condition on the initial density that ensures the mortality rate identifiability. In the inhomogeneous case, modeled by a non local boundary condition, we make explicit a sufficicent condition for the identifiability property, and give a condition for which the identifiability problem is ill-posed. We illustrate this latter case with numercial simulations

Mots clés: Parameter identifiability; population dynamics; age-structured model; transport PDE; non-local boundary condition

Domaines: Equations aux dérivées partielles [math.AP]

Antoine Perasso, Ulrich Razafison. Identifiability problem for recovering the mortality rate in an age-structured population dynamics model. 2014. ⟨hal-00995676⟩