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Stochastic population dynamics: The Poisson approximation

Solari, HG and Natiello, Mario LU (2003) In Physical Review E 67(3: 031918).
Abstract
We introduce an approximation to stochastic population dynamics based on almost independent Poisson processes whose parameters obey a set of coupled ordinary differential equations. The approximation applies to systems that evolve in terms of events such as death, birth, contagion, emission, absorption, etc., and we assume that the event-rates satisfy a generalized mass-action law. The dynamics of the populations is then the result of the projection from the space of events into the space of populations that determine the state of the system (phase space). The properties of the Poisson approximation are studied in detail. Especially, error bounds for the moment generating function and the generating function receive particular attention.... (More)
We introduce an approximation to stochastic population dynamics based on almost independent Poisson processes whose parameters obey a set of coupled ordinary differential equations. The approximation applies to systems that evolve in terms of events such as death, birth, contagion, emission, absorption, etc., and we assume that the event-rates satisfy a generalized mass-action law. The dynamics of the populations is then the result of the projection from the space of events into the space of populations that determine the state of the system (phase space). The properties of the Poisson approximation are studied in detail. Especially, error bounds for the moment generating function and the generating function receive particular attention. The deterministic approximation for the population fractions and the Langevin-type approximation for the fluctuations around the mean value are recovered within the framework of the Poisson approximation as particular limit cases. However, the proposed framework allows to treat other limit cases and general situations with small populations that lie outside the scope of the standard approaches. The Poisson approximation can be viewed as a general (numerical) integration scheme for this family of problems in population dynamics. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Physical Review E
volume
67
issue
3: 031918
publisher
American Physical Society
external identifiers
  • wos:000182020700070
  • scopus:84923224355
ISSN
1063-651X
DOI
language
English
LU publication?
yes
id
81f5d315-5e13-4c7a-918c-990abd3eeb11 (old id 313927)
date added to LUP
2007-09-22 11:40:32
date last changed
2018-05-29 12:00:40
@article{81f5d315-5e13-4c7a-918c-990abd3eeb11,
  abstract     = {We introduce an approximation to stochastic population dynamics based on almost independent Poisson processes whose parameters obey a set of coupled ordinary differential equations. The approximation applies to systems that evolve in terms of events such as death, birth, contagion, emission, absorption, etc., and we assume that the event-rates satisfy a generalized mass-action law. The dynamics of the populations is then the result of the projection from the space of events into the space of populations that determine the state of the system (phase space). The properties of the Poisson approximation are studied in detail. Especially, error bounds for the moment generating function and the generating function receive particular attention. The deterministic approximation for the population fractions and the Langevin-type approximation for the fluctuations around the mean value are recovered within the framework of the Poisson approximation as particular limit cases. However, the proposed framework allows to treat other limit cases and general situations with small populations that lie outside the scope of the standard approaches. The Poisson approximation can be viewed as a general (numerical) integration scheme for this family of problems in population dynamics.},
  author       = {Solari, HG and Natiello, Mario},
  issn         = {1063-651X},
  language     = {eng},
  number       = {3: 031918},
  publisher    = {American Physical Society},
  series       = {Physical Review E},
  title        = {Stochastic population dynamics: The Poisson approximation},
  url          = {http://dx.doi.org/},
  volume       = {67},
  year         = {2003},
}