6533b7ddfe1ef96bd127405e
RESEARCH PRODUCT
Identifiability problem for recovering the mortality rate in an age-structured population dynamics model
Antoine PerassoUlrich Razafisonsubject
age-structured modelAge structurePopulation35Q92 35R30 92D25 93B3001 natural sciencestransport PDE[ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP]Statisticspopulation dynamicsApplied mathematicsQuantitative Biology::Populations and Evolution[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]Boundary value problem0101 mathematicseducationMathematicseducation.field_of_studyParameter identifiabilityApplied MathematicsMortality rate010102 general mathematicsGeneral EngineeringInverse problemComputer Science Applications010101 applied mathematicsnon-local boundary conditionHomogeneousIdentifiabilitydescription
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, modelled by a non-local boundary condition, we make explicit a sufficient condition for the identifiability property, and give a condition for which the identifiability problem is ill-posed. We illustrate this latter case with numerical simulations.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2014-05-23 |