Stochastic modelling of age-structured population with time and size dependence of immigration rate

被引：2

作者：

Pichugin, Boris J. ^{[1
]}

Pertsev, Nikolai V. ^{[1
]}

Topchii, Valentin A. ^{[1
]}

Loginov, Konstantin K. ^{[1
]}

机构：

[1] Sobolev Inst Math SB RAS, Novosibirsk 630090, Russia

来源：

RUSSIAN JOURNAL OF NUMERICAL ANALYSIS AND MATHEMATICAL MODELLING | 2018年 / 33卷 / 05期

关键词：

Stochastic age-structured and size-dependent population model; branching stochastic processes with immigration; nonlinear immigration rate; non-exponential distribution of the lifespan of individuals; Monte Carlo simulation; STATISTICAL SIMULATION; LIVING SYSTEMS; HIV-INFECTION; DYNAMICS; EQUATIONS; FAMILY;

D O I：

10.1515/rnam-2018-0024

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A stochastic age-structured population model with immigration of individuals is considered. We assume that the lifespan of each individual is a random variable with a distribution function which may differ from the exponential one. The immigration rate of individuals depends on the time and total population size. Upper estimates for the mean and variance of the population size are established based on the theory of branching processes with constant immigration rate. A Monte Carlo simulation algorithm of population dynamics is developed. The results of numerical experiments with the model are presented.

引用

页码：289 / 299

页数：11

共 29 条

[1] Algorithms for exact and approximate statistical simulation of Poisson ensembles [J].

Averina, T. A. ;

Mikhailov, G. A. .

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2010, 50 (06) :951-962

[2] Individual and patch behaviour in structured metapopulation models [J].

Barbour, A. D. ;

Luczak, M. J. .

JOURNAL OF MATHEMATICAL BIOLOGY, 2015, 71 (03) :713-733

[3]

Bartlett M.S., 1955, INTRO STOCHASTIC PRO

[4]

Bharucha Reid A. T., 1960, ELEMENTS THEORY MARK

[5] Structured population models, conservation laws, and delay equations [J].

Bocharov, G ;

Hadeler, KP .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2000, 168 (01) :212-237

[6] Human Immunodeficiency Virus Infection: from Biological Observations to Mechanistic Mathematical Modelling [J].

Bocharov, G. ;

Chereshnev, V. ;

Gainova, I. ;

Bazhan, S. ;

Bachmetyev, B. ;

Argilaguet, J. ;

Martinez, J. ;

Meyerhans, A. .

MATHEMATICAL MODELLING OF NATURAL PHENOMENA, 2012, 7 (05) :78-104

[7] A Hierarchical Kinetic Theory of Birth, Death and Fission in Age-Structured Interacting Populations [J].

Chou, Tom ;

Greenman, Chris D. .

JOURNAL OF STATISTICAL PHYSICS, 2016, 164 (01) :49-76

[8] Delay differential systems for tick population dynamics [J].

Fan, Guihong ;

Thieme, Horst R. ;

Zhu, Huaiping .

JOURNAL OF MATHEMATICAL BIOLOGY, 2015, 71 (05) :1017-1048

[9] Stochastic modeling of stress erythropoiesis using a two-type age-dependent branching process with immigration [J].

Hyrien, O. ;

Peslak, S. A. ;

Yanev, N. M. ;

Palis, J. .

JOURNAL OF MATHEMATICAL BIOLOGY, 2015, 70 (07) :1485-1521

[10] AGE-DEPENDENT BRANCHING PROCESSES ALLOWING IMMIGRATION [J].

JAGERS, P .

THEORY OF PROBILITY AND ITS APPLICATIONS,USSR, 1968, 13 (02) :225-&

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