Session S12 - Delay and functional differential equations and applications

Tuesday, July 13, 11:05 ~ 11:40 UTC-3

Stochastic age-structured population models derived from the McKendrick-von Foerster equaton

Arkadi Ponossov

Norwegian University of Life Sciences, Norway   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

A widespread method of producing a stochastic population model consists in appending an additive stochastic noise to the model’s deterministic counterpart. It is shown in the talk that this straightforward construction may result in a wrong equation, at least in the case of age-structured population models derived from the McKendrick-von Foerster equaton (MFE), the biological “conservation law”. This well-elaborated transformation technique produces many popular deterministic differential equations with time-delay such as Nicholson’s blowflies model, the recruitment-delayed model etc.

If one takes MFE with a stochastically perturbed mortality rate as a starting point and use a similar transformation technique, then, as it is demonstrated in the talk, one obtains stochastic versions of the above population models, which are very different from those one can construct by simply appending an additive stochasticity to deterministic equations. In particular, it is shown that stochastic Nicholson’s blowflies model should contain both additive and multiplicative stochastic noises.

Joint work with Lev Idels (Vancouver Island University, Canada) and Ramazan Kadiev (Dagestan State University, Russian Federation).

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