Russian version English version
Volume 18   Issue 1   Year 2023
Pertsev N., Topchii V., Loginov K.

Stochastic Modeling of the Epidemic Process Based On a Stage-Dependent Model with Non-Markov Constraints for Individuals

Mathematical Biology & Bioinformatics. 2023;18(1):145-176.

doi: 10.17537/2023.18.145.


  1. Cooke K., Van Den Driessche P. Analysis of an SEIRS epidemic model with two delays. J. Math. Biol. 1996;35:240-260. doi: 10.1007/s002850050051
  2. Beretta E., Hara T., Ma W., Takeuchi Y. Global asymptotic stability of an SIR epidemic model with distributed time delay. Nonlin. Anal. 2001;47(6):4107-4115. doi: 10.1016/S0362-546X(01)00528-4
  3. Taylor M.L., Carr T.W. An SIR epidemic model with partial temporary immunity modeled with delay. J. Math. Biol. 2009;59:841-880. doi: 10.1007/s00285-009-0256-9
  4. Pertsev N.V., Pichugin B.Yu., Pichugina A.N. Analysis of the Asymptotic Behavior Solutions of Some Models of Epidemic Processes. Mathematical Biology and Bioinformatics. 2013;8(1):21-48. doi: 10.17537/2013.8.21
  5. Yuan Y., Belair J. Threshold dynamics in an SEIRS model with latency and temporary immunity. J. Math. Biol. 2014;69:875-904. doi: 10.1007/s00285-013-0720-4
  6. Barbarossa M.V., Rost G. Immuno-epidemiology of a population structured by immune status: a mathematical study of waning immunity and immune system boosting. J. Math. Biol. 2015;71:1737-1770. doi: 10.1007/s00285-015-0880-5
  7. Pertsev N.V., Loginov K.K., Topchii V.A. Analysis of an Epidemic Mathematical Model Based on Delay Differential Equations. J. Appl. Ind. Math. 2020;14:396-406. doi: 10.1134/S1990478920020167
  8. Pertsev N.V., Loginov K.K., Topchii V.A. Analysis of a Stage-Dependent Epidemic Model Based on a Non-Markov Random Process. J. Appl. Ind. Math. 2020;14:566-580. doi: 10.1134/S1990478920030151
  9. Pertsev N.V., Topchii V.A., Loginov K.K. Numerical stochastic modeling of dynamics of interacting populations. Sib. Zh. Ind. Mat. 2022;25(3):135-153. doi: 10.33048/SIBJIM.2021.25.312
  10. Loginov K., Pertsev N. Direct Statistical Modeling of Spread of Epidemic Based On a Stage-Dependent Stochastic Model. Mathematical Biology and Bioinformatics. 2021;16(2):169-200. doi: 10.17537/2021.16.169
  11. 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. Mathematical Biology and Bioinformatics. 2022;17(1):43-81. doi: 10.17537/2022.17.43
  12. 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
  13. Marchenko M. PARMONC – a software library for massively parallel stochastic simulation. Parallel Computing Technologies. Berlin; Heidelberg: Springer-Verl, 2011. P. 302-316. (Lecture Notes in Computer Science. V. 6873). doi: 10.1007/978-3-642-23178-0_27
  14. Mikhailov G.A., Voitishek A.V. Chislennoe statisticheskoe modelirovanie. Metody Monte-Karlo. (Numerical statistical modeling. Monte Carlo Methods). Moscow; 2006. 368 p. (in Russ.).
  15. Karlin S. Osnovy teorii sluchaynykh protsessov. Moscow.: Mir, 1971. 536 p. (Translation of: Karlin S. Foundations of the theory of random processes).
  16. Pertsev N.V., Topchii V.A., Loginov K.K. Numerical modelling of the transition of infected cells and virions between two lymph nodes in a stochastic model of HIV-1 infection. Russ. J. Numer. Anal. Math. Modelling. 2021;36(5):293-302. doi: 10.1515/rnam-2021-0024
  17. Mirasol N.M. The Output of an M/G/∞ Queuing System is Poisson. Operations Research. 1963;11(2):282-284. doi: 10.1287/opre.11.2.282
  18. Sevastyanov B.A. Branching Processes. Moscow: Nauka; 1971. 436 p. (in Russ.).
  19. Cramér H. Matematicheskie metody statistiki. Moscow, 1975. 648 p. (Translation of: Cramér H. Mathematical Methods of Statistics. Princeton University Press, 1946 doi: 10.1515/9781400883868).
Table of Contents Original Article
Math. Biol. Bioinf.
doi: 10.17537/2023.18.145
published in Russian

Abstract (rus.)
Abstract (eng.)
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