Age distribution dynamics with stochastic jumps in mortality


Conference Paper

© 2017 The Author(s) Published by the Royal Society. All rights reserved. While deterministic age distribution models have been extensively studied and applied in various disciplines, little work has been devoted to understanding the role of stochasticity in birth and mortality terms. In this paper, we analyse a stochastic M’Kendrick–von Foerster equation in which jumps in mortality represent intense losses of population due to external events. We present explicit solutions for the probability density functions of the age distribution and the total population and for the temporal dynamics of their moments. We also derive the dynamics of the mean age of the population and its harmonic mean. The framework is then used to calculate the age distribution of salt in the soil root zone, where the accumulation of salt by atmospheric deposition is counteracted by plant uptake and by jump losses due to percolation events.

Full Text

Duke Authors

Cited Authors

  • Calabrese, S; Porporato, A; Laio, F; Odorico, PD; Ridolfi, L

Published Date

  • November 1, 2017

Published In

Volume / Issue

  • 473 / 2207

Electronic International Standard Serial Number (EISSN)

  • 1471-2946

International Standard Serial Number (ISSN)

  • 1364-5021

Digital Object Identifier (DOI)

  • 10.1098/rspa.2017.0451

Citation Source

  • Scopus