On bilinear kinetic equations. Between micro and macro descriptions of biological populations

Mirosław Lachowicz. "On bilinear kinetic equations. Between micro and macro descriptions of biological populations." Banach Center Publications 63.1 (2003): 217-230. <http://eudml.org/doc/282191>.

@article{MirosławLachowicz2003,
abstract = {In this paper a general class of Boltzmann-like bilinear integro-differential systems of equations (GKM, Generalized Kinetic Models) is considered. It is shown that their solutions can be approximated by the solutions of appropriate systems describing the dynamics of individuals undergoing stochastic interactions (at the "microscopic level"). The rate of approximation can be controlled. On the other hand the GKM result in various models known in biomathematics (at the "macroscopic level") including the "SIR" model, some competitive systems and the Smoluchowski coagulation model.},
author = {Mirosław Lachowicz},
journal = {Banach Center Publications},
keywords = {stochastic particle systems; SIR model in epidemiology; logistic equation; models of coagulation},
language = {eng},
number = {1},
pages = {217-230},
title = {On bilinear kinetic equations. Between micro and macro descriptions of biological populations},
url = {http://eudml.org/doc/282191},
volume = {63},
year = {2003},
}

TY - JOUR
AU - Mirosław Lachowicz
TI - On bilinear kinetic equations. Between micro and macro descriptions of biological populations
JO - Banach Center Publications
PY - 2003
VL - 63
IS - 1
SP - 217
EP - 230
AB - In this paper a general class of Boltzmann-like bilinear integro-differential systems of equations (GKM, Generalized Kinetic Models) is considered. It is shown that their solutions can be approximated by the solutions of appropriate systems describing the dynamics of individuals undergoing stochastic interactions (at the "microscopic level"). The rate of approximation can be controlled. On the other hand the GKM result in various models known in biomathematics (at the "macroscopic level") including the "SIR" model, some competitive systems and the Smoluchowski coagulation model.
LA - eng
KW - stochastic particle systems; SIR model in epidemiology; logistic equation; models of coagulation
UR - http://eudml.org/doc/282191
ER -