Geodesic
Stochastic Modeling of Compartmental Systems with Pipes
Matematičeskaâ biologiâ i bioinformatika, Tome 14 (2019) no. 1, pp. 188-203.

Voir la notice de l'article provenant de la source Math-Net.Ru

An approach to the construction of a stochastic model of population dynamics distributed over a compartmental system with pipes is proposed. Population dynamics is described in terms of a multidimensional random process of birth and death, supplemented by taking into account point distributions reflecting different types of particles. In this model, the belonging of a particle to a certain type is determined by the time of its transition between compartments. The duration of particle transitions through the pipes are not random, but are set as parameters of the environment in which the population develops. Graph theory is used for formalization and compact representation of the model. On the basis of the Monte Carlo method the algorithm of numerical simulation of population dynamics is constructed. The results of computational experiments for a system consisting of five compartments are presented. 
@article{MBB_2019_14_1_a14,
     author = {K. K. Loginov and N. V. Pertsev and V. A. Topchii},
     title = {Stochastic {Modeling} of {Compartmental} {Systems} with {Pipes}},
     journal = {Matemati\v{c}eska\^a biologi\^a i bioinformatika},
     pages = {188--203},
     publisher = {mathdoc},
     volume = {14},
     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MBB_2019_14_1_a14/}
}
TY  - JOUR
AU  - K. K. Loginov
AU  - N. V. Pertsev
AU  - V. A. Topchii
TI  - Stochastic Modeling of Compartmental Systems with Pipes
JO  - Matematičeskaâ biologiâ i bioinformatika
PY  - 2019
SP  - 188
EP  - 203
VL  - 14
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MBB_2019_14_1_a14/
LA  - ru
ID  - MBB_2019_14_1_a14
ER  - 
%0 Journal Article
%A K. K. Loginov
%A N. V. Pertsev
%A V. A. Topchii
%T Stochastic Modeling of Compartmental Systems with Pipes
%J Matematičeskaâ biologiâ i bioinformatika
%D 2019
%P 188-203
%V 14
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MBB_2019_14_1_a14/
%G ru
%F MBB_2019_14_1_a14
K. K. Loginov; N. V. Pertsev; V. A. Topchii. Stochastic Modeling of Compartmental Systems with Pipes. Matematičeskaâ biologiâ i bioinformatika, Tome 14 (2019) no. 1, pp. 188-203. http://geodesic.mathdoc.fr/item/MBB_2019_14_1_a14/

[1] I. Gyori, J. Eller, “Compartmental Systems with Pipes”, Math. Biosc., 53 (1981), 223–247 | DOI | MR

[2] G. Bocharov, K. P. Hadeler, “Structured Population Models, Conservation Laws, and Delay Equations”, J. Diff. Equ., 168 (2000), 212–237 | DOI | MR | Zbl

[3] O. F. Voropaeva, Yu. I. Shokin, “Chislennoe modelirovanie v meditsine: Nekotorye postanovki zadach i rezultaty raschetov”, Vychislitelnye tekhnologii, 17:4 (2012), 29–55

[4] S. S. Simakov, “Sovremennye metody matematicheskogo modelirovaniya krovotoka c pomoschyu osrednennykh modelei”, Kompyuternye issledovaniya i modelirovanie, 10:5 (2018), 581–604 | DOI

[5] A. S. Mozokhina, S. I. Mukhin, “O kvaziodnomernom techenii zhidkosti s anizotropnoi vyazkostyu v sokraschayuschemsya sosude”, Differentsialnye uravneniya, 54:7 (2018), 956–962 | DOI | MR | Zbl

[6] S. Nakaoka, S. Iwami, K. Sato, “Dynamics of HIV infection in lymphoid tissue network”, J. Math. Biol., 72 (2016), 909–938 | DOI | MR | Zbl

[7] N. V. Pertsev, B. Yu. Pichugin, K. K. Loginov, “Stokhasticheskii analog modeli dinamiki VICh-1 infektsii, opisyvaemoi differentsialnymi uravneniyami s zapazdyvaniem”, Sibirskii zhurnal industrialnoi matematiki, 22:1 (2019), 74–89 | DOI | Zbl

[8] A. T. Barucha-Rid, Elementy teorii markovskikh protsessov i ikh prilozheniya, Nauka, M., 1969, 512 pp.

[9] O. Ore, Teoriya grafov, Nauka, M., 1968, 352 pp.

[10] T. Kharris, Teoriya vetvyaschikhsya sluchainykh protsessov, Mir, M., 1966, 356 pp.

[11] M. A. Marchenko, G. A. Mikhailov, “Parallel realization of statistical simulation and random number generators”, Russ. J. Numer. Anal. Math. Modelling, 17 (2002), 113–124 | DOI | MR | Zbl

[12] M. Marchenko, “PARMONC A Software Library for Massively Parallel Stochastic Simulation”, Parallel Computing Technologies, PaCT 2011, Lecture Notes in Computer Science, 6873, ed. Malyshkin V., Springer, Berlin–Heidelberg, 2011, 302–316 | DOI

[13] G. A. Mikhailov, A. V. Voitishek, Chislennoe statisticheskoe modelirovanie. Metody Monte-Karlo, Akademiya, M., 2006, 368 pp.

[14] B. A. Sevastyanov, “Ergodicheskaya teorema dlya markovskikh protsessov i ee prilozhenie k telefonnym sistemam s otkazami”, Teoriya veroyatnostei i ee primeneniya, 2:1 (1957), 106–116 | MR | Zbl

[15] T. L. Saati, Elementy teorii massovogo obsluzhivaniya i ee prilozheniya, Sovetskoe radio, M., 1965, 510 pp.

[16] N. M. Mirasol, “The Output of an $M/G/\infty$ Queuing Systems is Poisson”, Operat. Res., 11 (1963), 282–284 | DOI | Zbl

[17] F. R. Gantmakher, Teoriya matrits, 2-e izd., Nauka, M., 1966, 576 pp. | MR

[18] V. V. Voevodin, Yu. A. Kuznetsov, Matritsy i vychisleniya, Nauka, M., 1984, 320 pp. | MR

[19] G. Bocharov, V. Chereshnev, I. Gainova, S. Bazhan, B. Bachmetyev, J. Argilaguet, J. Martinez, A. Meyerhans, “Human Immunodeficiency Virus Infection: from Biological Observations to Mechanistic Mathematical Modelling”, Math. Model. Nat. Phenom., 7:5 (2012), 78–104 | DOI | MR | Zbl

[20] V. A. Chereshnev, G. A. Bocharov, A. V. Kim, S. I. Bazhan, I. A. Gainova, A. N. Krasovskii, N. G. Shmagel, A. V. Ivanov, M. A. Safronov, R. M. Tretyakova, Vvedenie v zadachi modelirovaniya i upravleniya dinamikoi VICh infektsii, Institut kompyuternykh issledovanii, M.–Izhevsk, 2016, 230 pp. | MR

[21] N. S. Bakhvalov, N. P. Zhidkov, G. M. Kobelkov, Chislennye metody, Nauka, M., 1987, 598 pp. | MR