Stochastic population dynamics: The Poisson approximation

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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, absorpt...

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Autores principales: Solari, H.G., Natiello, M.A.
Formato: JOUR
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_1063651X_v67_n3_p12_Solari
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_1063651X_v67_n3_p12_Solari2023-10-03T16:01:45Z Stochastic population dynamics: The Poisson approximation Solari, H.G. Natiello, M.A. 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. © 2003 The American Physical Society. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_1063651X_v67_n3_p12_Solari
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description 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. © 2003 The American Physical Society.
format JOUR
author Solari, H.G.
Natiello, M.A.
spellingShingle Solari, H.G.
Natiello, M.A.
Stochastic population dynamics: The Poisson approximation
author_facet Solari, H.G.
Natiello, M.A.
author_sort Solari, H.G.
title Stochastic population dynamics: The Poisson approximation
title_short Stochastic population dynamics: The Poisson approximation
title_full Stochastic population dynamics: The Poisson approximation
title_fullStr Stochastic population dynamics: The Poisson approximation
title_full_unstemmed Stochastic population dynamics: The Poisson approximation
title_sort stochastic population dynamics: the poisson approximation
url http://hdl.handle.net/20.500.12110/paper_1063651X_v67_n3_p12_Solari
work_keys_str_mv AT solarihg stochasticpopulationdynamicsthepoissonapproximation
AT natielloma stochasticpopulationdynamicsthepoissonapproximation
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