A spatial individual-based contact model with age structure

Dominika Jasińska

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica (2017)

  • Volume: 71, Issue: 1
  • ISSN: 0365-1029

Abstract

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The Markov dynamics of an infinite continuum birth-and-death system of point particles with age is studied. Each particle is characterized by its location x ∈ ℝ d and age a x ≥ 0 . The birth and death rates of a particle are age dependent. The states of the system are described in terms of probability measures on the corresponding configuration space. The exact solution of the  evolution equation for the correlation functions of first and second orders is found.

How to cite

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Dominika Jasińska. "A spatial individual-based contact model with age structure." Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica 71.1 (2017): null. <http://eudml.org/doc/289807>.

@article{DominikaJasińska2017,
abstract = {The Markov dynamics of an infinite continuum birth-and-death system of point particles with age is studied. Each particle is characterized by its location $x\in \mathbb \{R\}^d$ and age $a_x\ge 0$. The birth and death rates of a particle are age dependent. The states of the system are described in terms of probability measures on the corresponding configuration space. The exact solution of the  evolution equation for the correlation functions of first and second orders is found.},
author = {Dominika Jasińska},
journal = {Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica},
keywords = {Correlation function; contact model; birth and death model; configuration space; spatial individual-based model; Markov evolution; age structure},
language = {eng},
number = {1},
pages = {null},
title = {A spatial individual-based contact model with age structure},
url = {http://eudml.org/doc/289807},
volume = {71},
year = {2017},
}

TY - JOUR
AU - Dominika Jasińska
TI - A spatial individual-based contact model with age structure
JO - Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
PY - 2017
VL - 71
IS - 1
SP - null
AB - The Markov dynamics of an infinite continuum birth-and-death system of point particles with age is studied. Each particle is characterized by its location $x\in \mathbb {R}^d$ and age $a_x\ge 0$. The birth and death rates of a particle are age dependent. The states of the system are described in terms of probability measures on the corresponding configuration space. The exact solution of the  evolution equation for the correlation functions of first and second orders is found.
LA - eng
KW - Correlation function; contact model; birth and death model; configuration space; spatial individual-based model; Markov evolution; age structure
UR - http://eudml.org/doc/289807
ER -

References

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  5. Iannelli, M., Mathematical theory of age-structured population dynamics, Applied Mathematics Monographs, Giardini Editori e Stampatori, Pisa, 1995. 
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  7. Kondratiev, Y., Kutoviy, O., Pirogrov, S., Correlation functions and invariant measures in continuous contact model, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 11 (2) (2008), 231-258. 
  8. Kondratiev, Y., Lytvynov, E., Us, G., Analysis and geometry on ℝ + marked configuration spaces, Meth. Func. Anal. and Geometry 5 (1) (2006), 29-64. 
  9. Meleard, S., Tran, V., Trait substitution sequence process and canonical equation for age-structured populations, J. Math. Biol. 58 (6) (2009), 881-921. 
  10. Meleard, S., Tran, V., Slow and fast scales for superprocess limits of age-structured populations, Stochastic Process. Appl. 122 (1) (2012), 250-276. 
  11. Minlos, R. A., Lectures on statistical physics, Russian Mathematical Surveys 23 (1) (1968), 133-190. 
  12. Tanaś, A., A continuum individual based model of fragmentation: dynamics of correlation functions, Ann. Univ. Mariae Curie-Skłodowska Sect. A 64 (2) (2015), 73-83. 

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