On real-valued SDE and nonnegative-valued SDE population models with demographic variability.

Journal of Mathematical Biology
E J AllenH L Smith

Abstract

Population dynamics with demographic variability is frequently studied using discrete random variables with continuous-time Markov chain (CTMC) models. An approximation of a CTMC model using continuous random variables can be derived in a straightforward manner by applying standard methods based on the reaction rates in the CTMC model. This leads to a system of Itô stochastic differential equations (SDEs) which generally have the form [Formula: see text] where [Formula: see text] is the population vector of random variables, [Formula: see text] is the drift vector, and G is the diffusion matrix. In some problems, the derived SDE model may not have real-valued or nonnegative solutions for all time. For such problems, the SDE model may be declared infeasible. In this investigation, new systems of SDEs are derived with real-valued solutions and with nonnegative solutions. To derive real-valued SDE models, reaction rates are assumed to be nonnegative for all time with negative reaction rates assigned probability zero. This biologically realistic assumption leads to the derivation of real-valued SDE population models. However, small but negative values may still arise for a real-valued SDE model. This is due to the magnitudes of cer...Continue Reading

References

Jan 1, 1983·Journal of Mathematical Biology·I B Schwartz, H L Smith
Nov 25, 2003·Theoretical Population Biology·Linda J S Allen, Edward J Allen
Aug 10, 2012·Journal of Biological Dynamics·Linda J S Allen, Glenn E Lahodny
Jul 17, 2014·The Journal of Chemical Physics·David SchnoerrRamon Grima
Feb 28, 2016·Journal of Theoretical Biology·Yuanling NiuLuonan Chen

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Citations

Mar 24, 2021·Infectious Disease Modelling·Nika ShakibaLinda J S Allen

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