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Stochastic McKendrick–Von Foerster models with applications

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  • Ponosov, Arcady
  • Idels, Lev
  • Kadiev, Ramazan

Abstract

A newly presented McKendrick–Von Foerster model with a stochastically perturbed mortality rate is examined. A transformation method converting the model with non-local boundary conditions into a system of stochastic functional differential equations is offered. The method could be viewed as analogous to the one which is widely used for such type of deterministic problems. The derived stochastic functional differential equations yield multiple classic population models with ‘naturally born’ stochasticity, including delayed Nicholson’s blowflies, general recruitment and models with cannibalism, which by itself could be objects of future analysis and applications.

Suggested Citation

  • Ponosov, Arcady & Idels, Lev & Kadiev, Ramazan, 2020. "Stochastic McKendrick–Von Foerster models with applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    • Handle: RePEc:eee:phsmap:v:537:y:2020:i:c:s0378437119315092
    DOI: 10.1016/j.physa.2019.122641
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    References listed on IDEAS

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    1. Lin, Qiao-Feng & Wang, Can-Jun & Yang, Ke-Li & Tian, Meng-Yu & Wang, Ya & Dai, Jia-Liang, 2019. "Cross-correlated bounded noises induced the population extinction and enhancement of stability in a population growth model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1046-1057.
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    5. Avan, Jean & Grosjean, Nicolas & Huillet, Thierry, 2015. "Did the ever dead outnumber the living and when? A birth-and-death approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 277-292.
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    Cited by:

    1. Pasquali, Sara, 2021. "A stage structured demographic model with “no-regression” growth: The case of constant development rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    2. Pasquali, Sara & Trivellato, Barbara, 2023. "A stage structured demographic model with “no-regression” growth: The case of temperature-dependent development rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 629(C).

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