05.13.16 (Application of Computers and Mathematical Models in Science)
Keywords:
communities of interecting individuals, population dynamics, immunology, epidemiology, demography,
delay integral and differential equations,
random processes,
branching random processes,
Monte-Carlo method
creation a mathematical models of living systems, construction analytical and numerical methods for their analysis
Main publications:
Pertsev N.V., Loginov K.K., “Numerical stochastic modelling of the proliferation process of naive T-lymphocytes in the lymph node”, Russian Journal of Numerical
Analysis and Mathematical Modelling, 40:5 (2025), 405–417
Pertsev N.V., Topchii V.A., Loginov K.K., “Numerical Stochastic Simulation of Spatially Heterogeneous Population”, Numerical Analysis and Applications, 17:2 (2024), 174–187
Pertsev N.V., Topchii V.A., Loginov K.K., “Numerical Stochastic Modeling of Dynamics
of Interacting Populations”, Journal of Applied and Industrial Mathematics, 16:3 (2022), 524–539
Pertsev N., Loginov K , Bocharov G., “Nonlinear effects in the dynamics of HIV-1
infection predicted by mathematical model with multiple delays”, Discrete and Continuous
Dynamical Systems - Series S., 13:9 (2020), 2365–2384
Pertsev N.V., “Global solvability and estimates for solutions to the Cauchy
problem for the retarded functional differential equations that are used to the model living
systems”, Siberian Mathematical Journal, 59:1 (2018), 113–125
Pertsev, N.V.; Loginov, K.K., “Modeling the initial period of HIV-1 infection spread in the lymph node based on delay differential equations”, Computer Research and Modeling, 2025
2.
Pertsev, N.; Loginov, K., “Numerical Modeling of the Dynamics of HIV-1 Infection and T-cell Immune Response in the Lymph Node”, Mathematical Biology and Bioinformatics, 2025
3.
Pertsev, N.V., “Stability and Two-Sided Estimates of Solutions of a Linear Nonautonomous Differential Equation with Variable Delay”, Siberian Advances in Mathematics, 2025
4.
K. K. Loginov, N. V. Pertsev, “Stochastic modeling of HIV-1 infection dynamics in the lymph node taking into account contact interactions between CD4+ T-lymphocytes and dendritic cells”, Mat. Biolog. Bioinform., 20:2 (2025), 681–712
2024
5.
Pertsev, N.V.; Bocharov, G.A.; Loginov, K.K., “Mathematical Modeling of the Initial Period of Spread of HIV-1 Infection in the Lymphatic Node”, Mathematical Biology and Bioinformatics, 2024
2025
6.
Pertsev, N.V., “Stability of Solutions of Linear Systems of Differential Equations of Population Dynamics with Variable Delay”, Siberian Advances in Mathematics, 35 (2025), 50–62
2024
7.
Pertsev, N.V.; Loginov, K.K., “NUMERICAL MODELING OF THE EPIDEMIC PROCESS TAKING INTO ACCOUNT TIME- AND PLACE-LOCAL CONTACTS OF INDIVIDUALS”, Siberian Electronic Mathematical Reports, 2024
8.
N. V. Pertsev, V. A. Topchii, K. K. Loginov, “Numerical stochastic modeling of a spatially heterogeneous population”, Num. Anal. Appl., 17:2 (2024), 174–187
2023
9.
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 and Bioinformatics, 2023
10.
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 and Bioinformatics, 2023
11.
Topchii V.A., Pertsev N.V., “CRITICAL MULTITYPE BRANCHING PROCESSES ON A GRAPH AND THE MODEL OF THE HIV INFECTION DEVELOPMENT”, Siberian Electronic Mathematical Reports, 2023
12.
N. V. Pertsev, V. A. Topchii, K. K. Loginov, “Stochastic modeling of local by time and location contacts of individuals in the epidemic process”, J. Appl. Industr. Math., 17:2 (2023), 355–369
13.
N. V. Pertsev, K. K. Loginov, “Stochastic modeling in immunology based on a stage-dependent framework with non-Markov constraints for individual cell and pathogen dynamics”, Matem. biologiya i bioinform., 18:2 (2023), 543–567;
“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
15.
N. V. Pertsev, G. A. Bocharov, K. K. Loginov, “Numerical simulation of dynamics of T-lymphocytes population in the lymph node”, J. Appl. Industr. Math., 16:4 (2022), 737–750
16.
N. V. Pertsev, V. A. Topchii, K. K. Loginov, “Numerical stochastic modeling of dynamics of interacting populations”, J. Appl. Industr. Math., 16:3 (2022), 524–539
2021
17.
Loginov, K.; Pertsev, N., “Direct Statistical Modeling of Spread of Epidemic Based On a Stage-Dependent Stochastic Model”, Mathematical Biology and Bioinformatics, 2021
18.
N. V. Pertsev, K. K. Loginov, “Nakhozhdenie parametrov eksponentsialnykh otsenok reshenii zadachi Koshi dlya nekotorykh sistem lineinykh differentsialnykh uravnenii s zapazdyvaniem”, Sib. elektron. matem. izv., 18:2 (2021), 1307–1318
N. V. Pertsev, “Construction of exponentially decreasing estimates of solutions to a Cauchy problem for some nonlinear systems of delay differential equations”, Sib. elektron. matem. izv., 18:1 (2021), 579–598
20.
N. V. Pertsev, “Application of differential equations with variable delay in the compartmental models of living systems”, J. Appl. Industr. Math., 15:3 (2021), 466–482
21.
G. A. Bocharov, K. K. Loginov, N. V. Pertsev, V. A. Topchii, “Direct statistical modeling of HIV-1 infection based on a non-Markovian stochastic model”, Comput. Math. Math. Phys., 61:8 (2021), 1229–1251
2020
22.
K. K. Loginov, N. V. Pertsev, “Asimptoticheskoe povedenie reshenii integro-differentsialnogo uravneniya s zapazdyvaniem, voznikayuschego v modelyakh zhivykh sistem”, Matem. tr., 23:2 (2020), 122–147
N. V. Pertsev, K. K. Loginov, V. A. Topchii, “Analysis of a stage-dependent epidemic model based on a non-Markov random process”, J. Appl. Industr. Math., 14:3 (2020), 566–580
24.
N. V. Pertsev, K. K. Loginov, V. A. Topchii, “Analysis of an epidemic mathematical model based on delay differential equations”, J. Appl. Industr. Math., 14:2 (2020), 396–406
25.
N. V. Pertsev, “Exponential decay estimates for some components of solutions to the nonlinear delay differential equations of the living system models”, Siberian Math. J., 61:4 (2020), 715–724
2019
26.
K. K. Loginov, N. V. Pertsev, V. A. Topchii, “Stokhasticheskoe modelirovanie kompartmentnykh sistem s trubkami”, Matem. biologiya i bioinform., 14:1 (2019), 188–203
N. V. Pertsev, “Stability of linear delay differential equations arising in models of living systems”, Siberian Adv. Math., 30:1 (2020), 43–54
2019
28.
N. V. Pertsev, “Matrix stability and instability criteria for some systems of linear delay differential equations”, Siberian Electronic Mathematical Reports, 6 (2019), 876–885
29.
N. V. Pertsev, B. Yu. Pichugin, K. K. Loginov, “Stochastic analog of the dynamic model of HIV-1 infection described by delay differential equations”, J. Appl. Industr. Math., 13:1 (2019), 103–117
2018
30.
Nikolay V. Pertsev, Boris Yu. Pichugin, Anna N. Pichugina, “Application of M-matrices in studies of mathematical models of living systems”, Mathematical Biology and Bioinformatics, 13:1 (2018), 208-237 (to appear)
31.
Malygina, VV., Mulyukov, MV., Pertsev, NV., “On local asymptotic stability of a model of epidemic process”, Siberian Electronic Mathematical Reports, 15 (2018), 1301-1310
32.
N. V. Pertsev, “Global solvability and estimates of solutions to the Cauchy problem for the retarded functional differential equations that are used to model living systems”, Siberian Math. J., 59:1 (2018), 113–125
33.
N. V. Pertsev, B. Yu. Pichugin, A. N. Pichugina, “Application of M-matrices for the study of mathematical models of living systems”, Matem. biologiya i bioinform., 13:Suppl. (2018), 104–131;
N. V. Pertsev, B. Yu. Pichugin, A. N. Pichugina, “Investigation of solutions to one family of mathematical models of living systems”, Russian Math. (Iz. VUZ), 61:9 (2017), 48–60
35.
N. V. Pertsev, “Some properties of solutions to a family of integral equations arising in the models of living systems”, Siberian Math. J., 58:3 (2017), 525–535
2016
36.
Pertsev, NV; Pichugin, BY ; Pichugina, AN, “The correctness of a family of integral and delay differential equations, used in models of living systems”, Siberian Electronic Mathematical Reports, 13 (2016), 815-828
2015
37.
N. V. Pertsev, “Issledovanie reshenii matematicheskikh modelei epidemicheskikh protsessov, obladayuschikh obschimi strukturnymi svoistvami”, Sib. zhurn. industr. matem., 18:2 (2015), 85–98
V.N. Leonenko , N.V. Pertsev , Marc Artzrouni, “Using high performance algorithms for the hybrid simulation of disease dynamics on CPU and GPU”, 15th Annual International Conference on Computational Science (ICCS) 2015 (Reykjavik Univ, Reykjavik, ICELAND. JUN 01-03, 2015), Procedia Computer Science, 51, eds. Koziel, S, Elsevier, 2015, 150-159
Malygina, VV; Mulyukov, MV and Pertsev, NV, “On the local stability of a population dynamics model with delay”, Siberian Electronic Mathematical Reports, 11 (2014), 951-957
40.
N. V. Pertsev, “Nepreryvno-diskretnaya model rasprostraneniya i kontrolya tuberkuleza”, Sib. zhurn. industr. matem., 17:3 (2014), 86–97
N. V. Pertsev, B. Yu. Pichugin, A. N. Pichugina, “Issledovanie asimptoticheskogo povedeniya reshenii nekotorykh modelei epidemicheskikh protsessov”, Matem. biologiya i bioinform., 8:1 (2013), 21–48
N. V. Pertsev, “Application of M-matrices in construction of exponential estimates for solutions to the Cauchy problem for systems of linear difference and differential equations”, Siberian Adv. Math., 24:4 (2014), 240–260
2013
43.
N. V. Pertsev, “Two-sided estimates for solutions to the Cauchy problem for Wazewski linear differential systems with delay”, Siberian Math. J., 54:6 (2013), 1088–1097
2012
44.
N. V. Pertsev and V. N. Leonenko, “Discrete stochastic model of HIV infection spread within a heterogeneous population”, Russian Journal of Numerical Analysis and Mathematical Modelling, 27:5 (2012), 459-478
Pertsev, NV (Pertsev, N. V.) ; Leonenko, VN (Leonenko, V. N.), “Discrete stochastic model of HIV infection spread within a heterogeneous population”, Russian Journal of Numerical Analysis and Mathematical Modelling, 27:5 (2012), 459-477
2011
46.
N. V. Pertsev, G. E. Tsaregorodtseva, “Modeling population dynamics under the influence of harmful substances on the individual reproduction process”, Autom. Remote Control, 72:1 (2011), 129–140
47.
N. V. Pertsev, K. K. Loginov, “Stokhasticheskaya model dinamiki biologicheskogo soobschestva v usloviyakh potrebleniya osobyami vrednykh pischevykh resursov”, Matem. biologiya i bioinform., 6:1 (2011), 1–13
N. V. Pertsev, B. Yu. Pichugin, K. K. Loginov, “Statisticheskoe modelirovanie dinamiki populyatsii, razvivayuschikhsya v usloviyakh vozdeistviya toksichnykh veschestv”, Sib. zhurn. industr. matem., 14:2 (2011), 84–94
V. N. Leonenko, N. V. Pertsev, “Analiz effektivnosti programm vyyavleniya individuumov, predraspolozhennykh k kolorektalnomu raku, na osnove imitatsionnogo modelirovaniya”, UBS, 35 (2011), 207–236
N. V. Pertsev, G. E. Tsaregorodtseva, “A mathematical model for the dynamics of a population affected by pollutants”, J. Appl. Industr. Math., 5:1 (2011), 94–103
2010
51.
Pertsev, N.V., Pichugin, B.Y., “An individual-based stochastic model of the spread of tuberculosis”, J. Appl. Ind. Math., 4 (2010), 359–370
2005
52.
R. O. Karelina, N. V. Pertsev, “Postroenie dvustoronnikh otsenok dlya reshenii nekotorykh sistem differentsialnykh uravnenii s posledeistviem”, Sib. zhurn. industr. matem., 8:4 (2005), 60–72
N. V. Pertsev, A. N. Pichugina, B. Yu. Pichugin, “Povedenie reshenii dissipativnoi integralnoi modeli Lotki–Volterra”, Sib. zhurn. industr. matem., 6:2 (2003), 95–106
N. V. Pertsev, “Primenenie monotonnogo metoda i $M$-matrits k analizu povedeniya reshenii nekotorykh modelei biologicheskikh protsessov”, Sib. zhurn. industr. matem., 5:4 (2002), 110–122
N. V. Pertsev, “Two-sided estimates for solutions of an integrodifferential equation that describes the hematogenic process”, Russian Math. (Iz. VUZ), 45:6 (2001), 55–59
1999
56.
N. V. Pertsev, “On solutions of the Lotka–Volterra model taking into account the boundedness of the life spans of species of competing populations”, Differ. Equ., 35:9 (1999), 1201–1207
57.
N. V. Pertsev, “On bounded solutions of a class of systems of integral equations that arise in models of biological processes”, Differ. Equ., 35:6 (1999), 835–840
58.
N. V. Pertsev, “On the stability of the zero solution of a system of integrodifferential equations that arise in models of population dynamics”, Russian Math. (Iz. VUZ), 43:8 (1999), 44–49
59.
N. V. Pertsev, “Issledovanie reshenii integralnoi modeli Lotki–Volterra”, Sib. zhurn. industr. matem., 2:2 (1999), 153–167
N. V. Pertsev, “On the asymptotic behavior of solutions of a system of linear differential equations with delay”, Russian Math. (Iz. VUZ), 40:9 (1996), 45–49
1988
61.
I. Győri, N. V. Pertsev, “Stability of the equilibrium states of functional-differential equations of retarded type that have the property of mixed monotonicity”, Dokl. Math., 36:3 (1988), 404–407
2025
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