Russian version English version
Volume 18   Issue 2   Year 2023
Pertsev N.V., Loginov K.K.

Stochastic Modeling in Immunology Based On a Stage-Dependent Framework with Non-Markov Constraints for Individual Cell and Pathogen Dynamics

Mathematical Biology & Bioinformatics. 2023;18(2):543-567.

doi: 10.17537/2023.18.543.


  1. Marchuk G.I. Mathematical Models in Immunology. Numerical Methods and Experiments. Moscow: Nauka, 1991. 300 p.
  2. Banks H.T., Bortz D.M. A parameter sensitivity methodology in the context of HIV delay equation models. J. Math. Biol. 2005;50:607-625. doi: 10.1007/s00285-004-0299-x
  3. Pawelek K.A., Liu S., Pahlevani F., Rong L. A model of HIV-1 infection with two time delays: mathematical analysis and comparison with patient data. Math. Biosci. 2012;235(1):98-109. doi: 10.1016/j.mbs.2011.11.002
  4. Luzyanina T., Cupovic J., Ludewig B., Bocharov G. Mathematical models for CFSE labelled lymphocyte dynamics: asymmetry and time-lag in division. J. Math. Biol. 2014;69:1547-1583. doi: 10.1007/s00285-013-0741-z
  5. Pitchaimani M., Monica C. Global stability analysis of HIV-1 infection model with three time delays. J. Appl. Math. Comput. 2015;48:293-319. doi: 10.1007/s12190-014-0803-4
  6. Nechepurenko Yu., Khristichenko M., Grebennikov D., Bocharov G. Bistability analysis of virus infection models with time delays. Disc. Cont. Dyn. Syst. - Series S. 2020;13(9):2385-2401. doi: 10.3934/dcdss.2020166
  7. Pertsev N., Loginov K., Bocharov G. Nonlinear effects in the dynamics of HIV-1 infection predicted by mathematical model with multiple delays. Disc. Cont. Dyn. Syst. - Series S. 2020;13(9):2365-2384. doi: 10.3934/dcdss.2020141
  8. Pertsev N.V., Bocharov G.A., Loginov K.K. Numerical Simulation of T-Lymphocyte Population Dynamics in a Lymph Node. J. Appl. Ind. Math. 2022;16(4):737-750. doi: 10.1134/S1990478922040147
  9. Pichugin B.J., Pertsev N.V., Topchii V.A., Loginov K.K. Stochastic modeling of age-structured population with time and size dependence of immigration rate. Russ. J. Numer. Anal. Math. Model. 2018;33(5):289-299. doi: 10.1515/rnam-2018-0024
  10. Pertsev N.V., Pichugin B.Y., Loginov K.K. Stochastic Analog of the Dynamic Model of HIV-1 Infection Described by Delay Differential Equations. J. Appl. Ind. Math. 2019;13(1):103-117. doi: 10.1134/S1990478919010125
  11. Bocharov G.A., Loginov K.K., Pertsev N.V., Topchii V.A. Direct statistical modeling of HIV-1 infection based on a non-Markovian stochastic model. Comp. Math. and Math. Phys. 2021;61(8):1229-1251. doi: 10.1134/S0965542521060026
  12. Barbour A.D., Luczak M.J. Individual and patch behaviour in structured metapopulation models. J. Math. Biol. 2015;71(3):713-733. doi: 10.1007/s00285-014-0834-3
  13. Hyrien O., Peslak S.A., Yanev N.M., Palis J. Stochastic modeling of stress erythropoiesis using a two-type age-dependent branching process with immigration. J. Math. Biol. 2015;70(7):1485-1521. doi: 10.1007/s00285-014-0803-x
  14. Chou T., Greenman C.D. A Hierarchical Kinetic Theory of Birth, Death and Fission in Age-Structured Interacting Populations. J. Stat. Phys. 2016;164(1):49-76. doi: 10.1007/s10955-016-1524-x
  15. Konstantin K. Loginov, Nikolay V. Pertsev, Valentin A. Topchii. Stochastic Modeling of Compartmental Systems with Pipes. Math. Biol. Bioinf. 2019;14(1):188-203. doi: 10.17537/2019.14.188
  16. Pertsev N., Loginov K., Lukashev A., Vakulenko Yu. Stochastic Modeling of Dynamics of the Spread of COVID-19 Infection Taking Into Account the Heterogeneity of Population According To Immunological, Clinical and Epidemiological Criteria. Math. Biol. Bioinf. 2022;17(1):43-81. doi: 10.17537/2022.17.43
  17. Pertsev N., Topchii V., Loginov K. Stochastic Modeling of the Epidemic Process Based On a Stage-Dependent Model with Non-Markov Constraints for Individuals. Math. Biol. Bioinf. 2023;18(1):145-176. doi: 10.17537/2023.18.145
  18. Geehman I.I., Skorohod A.V. Introduction to the Theory of Random Processes. Moscow: Nauka, 1977. 568 p.
  19. Marchenko M.A., Mikhailov G.A. Parallel realization of statistical simulation and random number generators. Russ. J. Numer. Anal. Math. Model. 2002;17(1):113-124. doi: 10.1515/rnam-2002-0107
  20. Marchenko M. PARMONC - A Software Library for Massively Parallel Stochastic Simulation. Parallel Computing Technologies. Berlin, Heidelberg: Springer-Verl. 2011;6873:302-316. (Lecture Notes in Computer Science). doi: 10.1007/978-3-642-23178-0_27
  21. Mikhailov G.A., Voitishek A.V. Numerical Statistical Simulation. Monte-Carlo Methods. Moscow: Akademia, 2006. 367 p.
  22. Pertsev N.V., Pichugin B.J., Pichugina A.N. Investigation of solutions to one family of mathematical models of living systems. Russian Math. 2017;61(9):48-60. doi: 10.3103/S1066369X17090067
  23. Kramer G. Mathematical Methods of Statistics. Princeton: Princeton Univ. Press, 1999. 575 p.
  24. Abbas A.K., Likhtman A.H., Pillai S. Basic Immunology. Functions and Disorders of the Immune System. Moscow: Geotar Media, 2022. 404 p.
  25. Sattentau Q.J., Stevenson M. Macrophages and HIV-1: An Unhealthy Constellation. Cell Host $&$ Microbe. 2016;19(3):304-310. doi: 10.1016/j.chom.2016.02.013
  26. Dimopoulos Y., Moysi E., Petrovas C. The Lymph Node in HIV Pathogenesis. Curr. HIV/AIDS Rep. 2017;14:133-140. doi: 10.1007/s11904-017-0359-7
  27. Sevastijanov B.A. Branching Processes. Moscow: Nauka, 1971. 436 p.
  28. Jagers P. Branching Processes with Biological Applications. New York: Wiley, 1975. 268 p.
  29. Pertsev N.V. Stability of Linear Delay Differential Equations Arising in Models of Living Systems. Sib. Adv. Math. 2020;30(1):43-54. doi: 10.3103/S1055134420010046
  30. Kolmanovskii V.B., Nosov V.R. Stability and Periodic Modes of Regulated Systems with Delay. Moscow: Nauka, 1981. 448 p.
Table of Contents Original Article
Math. Biol. Bioinf.
doi: 10.17537/2023.18.543
published in English

Abstract (eng.)
Abstract (rus.)
Full text (eng., pdf)


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