Geodesic
Stochastic modeling of the epidemic process based on a stage-dependent model with non-Markov constraints for individuals
Matematičeskaâ biologiâ i bioinformatika, Tome 18 (2023) no. 1, pp. 145-176.

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

A continuous-discrete stochastic model of the epidemic process is presented. The model takes into account several stages of the development of an infectious disease, as well as the distributions of the durations of stay of individuals in these stages. The variables of the model are integer random variables that denote the quantity of individuals in cohorts, and sets of unique types of individuals that take into account the current state and history of stay of individuals in the stages of development of an infectious disease, distributions of durations of these stages are different from exponential or geometric. The results of an analytical and numerical research of the dynamics of the epidemic process are presented. The probabilities of infection eradication during a finite period of time are examined, depending on the numerical values of the infection spread coefficient and the distributions of the durations of the latent stage of the disease and the stage of preservation of immunity to infection. 
@article{MBB_2023_18_1_a11,
     author = {N. V. Pertsev and V. A. Topchii and K. K. Loginov},
     title = {Stochastic modeling of the epidemic process based on a stage-dependent model with {non-Markov} constraints for individuals},
     journal = {Matemati\v{c}eska\^a biologi\^a i bioinformatika},
     pages = {145--176},
     publisher = {mathdoc},
     volume = {18},
     number = {1},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MBB_2023_18_1_a11/}
}
TY  - JOUR
AU  - N. V. Pertsev
AU  - V. A. Topchii
AU  - K. K. Loginov
TI  - Stochastic modeling of the epidemic process based on a stage-dependent model with non-Markov constraints for individuals
JO  - Matematičeskaâ biologiâ i bioinformatika
PY  - 2023
SP  - 145
EP  - 176
VL  - 18
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MBB_2023_18_1_a11/
LA  - ru
ID  - MBB_2023_18_1_a11
ER  - 
%0 Journal Article
%A N. V. Pertsev
%A V. A. Topchii
%A K. K. Loginov
%T Stochastic modeling of the epidemic process based on a stage-dependent model with non-Markov constraints for individuals
%J Matematičeskaâ biologiâ i bioinformatika
%D 2023
%P 145-176
%V 18
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MBB_2023_18_1_a11/
%G ru
%F MBB_2023_18_1_a11
N. V. Pertsev; V. A. Topchii; K. K. Loginov. Stochastic modeling of the epidemic process based on a stage-dependent model with non-Markov constraints for individuals. Matematičeskaâ biologiâ i bioinformatika, Tome 18 (2023) no. 1, pp. 145-176. http://geodesic.mathdoc.fr/item/MBB_2023_18_1_a11/

[1] K. Cooke, P. Van Den Driessche, “Analysis of an SEIRS epidemic model with two delays”, J. Math. Biol., 1996, no. 35, 240–260 | DOI | MR | Zbl

[2] E. Beretta, T. Hara, W. Ma, Y. Takeuchi, “Global asymptotic stability of an SIR epidemic model with distributed time delay”, Nonlin. Anal., 47:6 (2001), 4107–4115 | DOI | MR | Zbl

[3] M. L. Taylor, T. W. Carr, “An SIR epidemic model with partial temporary immunity modeled with delay”, J. Math. Biol, 2009, no. 59, 841–880 | DOI | MR | Zbl

[4] N. V. Pertsev, B. Yu. Pichugin, A. N. Pichugina, “Issledovanie asimptoticheskogo povedeniya reshenii nekotorykh modelei epidemicheskikh protsessov”, Mat. biologiya i bioinformatika, 8:1 (2013), 21–48 | DOI | MR

[5] Y. Yuan, J. Belair, “Threshold dynamics in an SEIRS model with latency and temporary immunity”, J. Math. Biol, 2014, no. 69, 875–904 | DOI | MR | Zbl

[6] M. V. Barbarossa, G. Rost, “Immuno-epidemiology of a population structured by immune status: a mathematical study of waning immunity and immune system boosting”, J. Math. Biol, 2015, no. 71, 1737–1770 | DOI | MR | Zbl

[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., 14 (2020), 396-406 | DOI | MR | Zbl

[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., 14 (2020), 566–580 | DOI | MR | Zbl

[9] N. V. Pertsev, V. A. Topchii, K. K. Loginov, “Chislennoe stokhasticheskoe modelirovanie dinamiki vzaimodeistvuyuschikh populyatsii”, Sib. zhurn. ind. mat, 25:3 (2022), 135–153 | DOI | Zbl

[10] K. K. Loginov, N. V. Pertsev, “Pryamoe statisticheskoe modelirovanie rasprostraneniya epidemii na osnove stadiya-zavisimoi stokhasticheskoi modeli”, Mat. biologiya i bioinformatika, 16:2 (2021), 169–200 | DOI

[11] N. V. Pertsev, K. K. Loginov, A. N. Lukashev, Yu. A. Vakulenko, “Stokhasticheskoe modelirovanie dinamiki rasprostraneniya Kovid-uchetom neodnorodnosti naseleniya po immunologicheskim, klinicheskim i epidemiologicheskim kriteriyam”, Mat. biologiya i bioinformatika, 17:1 (2022), 43–81, 19 pp. | DOI | MR

[12] 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

[13] M. Marchenko, “PARMONC a software library for massively parallel stochastic simulation”, Parallel Computing Technologies, Lecture Notes in Computer Science, 6873, Springer-Verl, Berlin–Heidelberg, 2011, 302–316 | DOI

[14] G. A. Mikhailov, A. V. Voitishek, “Chislennoe statisticheskoe modelirovanie”, Metody Monte-Karlo, 2006, Akademiya, M.

[15] S. Karlin, Osnovy teorii sluchainykh protsessov, Mir, M., 1971

[16] N. V. Pertsev, V. A. Topchii, K. K. Loginov, “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, 36:5 (2021), 293–302 | DOI | MR | Zbl

[17] N. M. Mirasol, “The Output of an $M/G/\infty$ Queuing System is Poisson”, Operations Research, 11:2 (1963), 282–284 | DOI | Zbl

[18] Sevastyanov B. A., Vetvyaschiesya protsessy, Nauka, M., 1971

[19] G. Kramer, Matematicheskie metody statistiki, Mir, M., 1975