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.
References
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- Mikhailov G.A., Voitishek A.V. Chislennoe statisticheskoe modelirovanie. Metody Monte-Karlo. (Numerical statistical modeling. Monte Carlo Methods). Moscow; 2006. 368 p. (in Russ.).
- Karlin S. Osnovy teorii sluchaynykh protsessov. Moscow.: Mir, 1971. 536 p. (Translation of: Karlin S. Foundations of the theory of random processes).
- 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
- 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
- Sevastyanov B.A. Branching Processes. Moscow: Nauka; 1971. 436 p. (in Russ.).
- 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).
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