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Том 14   Выпуск 1   Год 2019
Логинов Константин Константинович, Перцев Николай Викторович, Топчий Валентин Алексеевич

Стохастическое моделирование компартментных систем с трубками

Математическая биология и биоинформатика. 2019;14(1):188-203.

doi: 10.17537/2019.14.188.

Список литературы

 

  1. Gyori I., Eller J. Compartmental Systems with Pipes. Math. Biosc. 1981;53:223-247. doi: 10.1016/0025-5564(81)90019-5
  2. Bocharov G., Hadeler K.P. Structured Population Models, Conservation Laws, and Delay Equations. J. Diff. Equ. 2000;168:212-237. doi: 10.1006/jdeq.2000.3885
  3. Voropayeva O.F., Shokin Yu.I. Numerical simulation in medicine: formulations of the problems and some results of calculations. Computational Technologies. 2012;17(4):29-55 (in Russ.).
  4. Simakov S.S. Modern methods of mathematical modeling of blood flow using reduced order methods. Computer Research and Modeling. 2018;10(5):581-604 (in Russ.). doi: 10.20537/2076-7633-2018-10-5-581-604
  5. Mozokhina A.S., Mukhin S.I. Quasi-one-dimensional flow of a fluid with anisotropic viscosity in a pulsating vessel. Differential Equations. 2018;54(7):938-944. doi: 10.1134/S0374064118070129
  6. Nakaoka S., Iwami S., Sato K. Dynamics of HIV infection in lymphoid tissue network. J. Math. Biol. 2016;72:909-938. doi: 10.1007/s00285-015-0940-x
  7. Pertsev N.V., Pichugin B.Yu., Loginov K.K. Stochastic analog of the dynamic model of HIV-1 infection described by delay differential equations. Sib. Zh. Ind. Mat. 2019;22(1):74-89 (in Russ.).
  8. Bharucha-Reid A.T. Elements of the Theory of Markov Processes and Their Applications. New York: McGraw‐Hill; 1960. (Dover Books on Mathematics).
  9. Ore O. Theory of Graphs. American Mathematical Society, 1962. 270 p. doi: 10.1090/coll/038
  10. Harris T.E. The theory of branching processes. 1964. doi: 10.1007/978-3-642-51866-9
  11. Marchenko M.A., Mikhailov G.A. Parallel realization of statistical simulation and random number generators. Russ. J. Numer. Anal. Math. Modelling. 2002;17:113-124. doi: 10.1515/rnam-2002-0107
  12. Marchenko M. PARMONC - A Software Library for Massively Parallel Stochastic Simulation. In: Parallel Computing Technologies. PaCT 2011. Lecture Notes in Computer Science. Ed. Malyshkin V. Berlin, Heidelberg: Springer, 2011. V. 6873. P. 302-316.
  13. Mikhailov G.A., Voitishek A.V. Chislennoe statisticheskoe modelirovanie. Metody Monte-Karlo (Numerical statistical modeling. Monte Carlo methods). Moscow, 2006. 368 p. (in Russ.).
  14. Sevast'yanov B.A. An Ergodic Theorem for Markov Processes and Its Application to Telephone Systems with Refusals. Theory of Probability and its Applications. 1957;2(1):104–112. doi: 10.1137/1102005
  15. Saaty T.L. Elementy teorii massovogo obsluzhivaniia i ee prilozheniia. Moscow, 1965. 510 p. (Translation of: Saaty T.L. Elements of Queuing Theory. With Applications. New-York: Mc-Graw-Hill, 1961. 423 p.).
  16. Mirasol N.M. The Output of an M/G/∞ Queuing Systems is Poisson. Operat. Res. 1963;11:282-284. doi: 10.1287/opre.11.2.282
  17. Gantmacher F.R Teoriia matrits.Moscow, 1966. 576 p. (Translation of: Gantmacher F.R. The Theory of Matrices. New-York: Chelsea Publishing Company, 1959).
  18. Voevodin V.V., Kuznetsov Iu.A. Matritsy i vychisleniia (Matrices and calculations). Moscow, 1984. 320 p. (in Russ.).
  19. Bocharov G., Chereshnev V., Gainova I., Bazhan S., Bachmetyev B., Argilaguet J., Martinez J., Meyerhans A. Human Immunodeficiency Virus Infection: from Biological Observations to Mechanistic Mathematical Modelling. Math. Model. Nat. Phenom. 2012;7(5):78-104. doi: 10.1051/mmnp/20127507
  20. Chereshnev V.A., Bocharov G.A., Kim A.V., Bazhan S.I., Gainova I.A., Krasovskii A.N., Shmagel' N.G., Ivanov A.V., Safronov M.A., Tret'iakova R.M. Vvedenie v zadachi modelirovaniia i upravleniia dinamikoi VICh infektsii (Introduction to the tasks of modeling and managing the dynamics of HIV infection). Moscow, 2016. 230 p. (in Russ.).
  21. Bakhvalov N.S., Zhidkov N.P., Kobel'kov G.M. Chislennye metody (Numerical Methods). Moscow, 1987. 598 p. (in Russ.).
Содержание Оригинальная статья
Мат. биол. и биоинф.
2019;14(1):188-203
doi: 10.17537/2019.14.188
опубликована на рус. яз.

Аннотация (рус.)
Аннотация (англ.)
Полный текст (рус., pdf)
Список литературы

 

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