Age distribution dynamics with stochastic jumps in mortality

Salvatore Calabrese, Amilcare Michele M. Porporato, Francesco Laio, Paolo D. Odorico, Luca Ridolfi

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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.

Original languageEnglish (US)
Article number20170451
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2207
StatePublished - Nov 1 2017

All Science Journal Classification (ASJC) codes

  • General Engineering
  • General Physics and Astronomy
  • General Mathematics


  • Age distribution dynamics
  • M’Kendrick–von Foerster equation
  • Poisson jumps
  • Stochastic mortality
  • Stochastic soil salinity


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