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., “Conditions of Well-Posedness of Integral Models of Some Living Systems”, Differential Equations, 53:9 (2017), 1127–1144
Pertsev N.V., “Study of solutions of continuous-discrete model of HIV infection spread”, Russian Journal of Numerical Analysis and Mathematical Modelling, 31:5 (2016), 281–291
N. V. Pertsev, V. N. Leonenko, “Analysis of a stochastic model for the spread of tuberculosis with regard to reproduction and seasonal immigration of individuals”, Russian Journal of Numerical Analysis and Mathematical Modelling, 29:5 (2014), 285–295
N. V. Pertsev, V. A. Topchii, K. K. Loginov, “Numerical stochastic modeling of a spatially heterogeneous population”, Sib. Zh. Vychisl. Mat., 27:2 (2024), 217–232
2023
2.
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”, Mat. Biolog. Bioinform., 18:2 (2023), 543–567
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”, Mat. Biolog. Bioinform., 18:1 (2023), 145–176
V. A. Topchii, N. V. Pertsev, “Critical Multitype Branching Processes on a Graph and the Model of the HIV Infection Development”, Sib. Èlektron. Mat. Izv., 20:1 (2023), 465–476
N. V. Pertsev, V. A. Topchii, K. K. Loginov, “Stochastic modeling of local by time and location contacts of individuals in the epidemic process”, Sib. Zh. Ind. Mat., 26:2 (2023), 94–112; J. Appl. Industr. Math., 17:2 (2023), 355–369
2022
6.
N. V. Pertsev, K. K. Loginov, A. N. Lukashev, Yu. A. Vakulenko, “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”, Mat. Biolog. Bioinform., 17:1 (2022), 43–81
N. V. Pertsev, G. A. Bocharov, K. K. Loginov, “Numerical simulation of dynamics of T-lymphocytes population
in the lymph node”, Sib. Zh. Ind. Mat., 25:4 (2022), 136–152
8.
N. V. Pertsev, V. A. Topchii, K. K. Loginov, “Numerical stochastic modeling of dynamics of interacting populations”, Sib. Zh. Ind. Mat., 25:3 (2022), 135–153
K. K. Loginov, N. V. Pertsev, “Direct statistical modeling of spread of epidemic based on a stage-dependent stochastic model”, Mat. Biolog. Bioinform., 16:2 (2021), 169–200
N. V. Pertsev, K. K. Loginov, “Finding the parameters of exponential estimates of solutions to the Cauchy problem for some systems of linear delay differential equations”, Sib. Èlektron. Mat. Izv., 18:2 (2021), 1307–1318
11.
N. V. Pertsev, “Construction of exponentially decreasing estimates of solutions to a Cauchy problem for some nonlinear systems of delay differential equations”, Sib. Èlektron. Mat. Izv., 18:1 (2021), 579–598
12.
N. V. Pertsev, “Application of differential equations with variable delay in the compartmental models of living systems”, Sib. Zh. Ind. Mat., 24:3 (2021), 55–73
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”, Zh. Vychisl. Mat. Mat. Fiz., 61:8 (2021), 1245–1268; Comput. Math. Math. Phys., 61:8 (2021), 1229–1251
K. K. Loginov, N. V. Pertsev, “Асимптотическое поведение решений интегро-дифференциального уравнения с запаздыванием, возникающего в моделях живых систем”, Mat. Tr., 23:2 (2020), 122–147
15.
N. V. Pertsev, K. K. Loginov, V. A. Topchii, “Analysis of a stage-dependent epidemic model based on a non-Markov random process”, Sib. Zh. Ind. Mat., 23:3 (2020), 105–122; J. Appl. Industr. Math., 14:3 (2020), 566–580
N. V. Pertsev, K. K. Loginov, V. A. Topchii, “Analysis of an epidemic mathematical model based on delay differential equations”, Sib. Zh. Ind. Mat., 23:2 (2020), 119–132; J. Appl. Industr. Math., 14:2 (2020), 396–406
N. V. Pertsev, “Exponential decay estimates for some components of solutions to the nonlinear delay differential equations of the living system models”, Sibirsk. Mat. Zh., 61:4 (2020), 901–912; Siberian Math. J., 61:4 (2020), 715–724
N. V. Pertsev, “Stability of linear delay differential equations arising in models of living systems”, Mat. Tr., 22:2 (2019), 157–174; Siberian Adv. Math., 30:1 (2020), 43–54
N. V. Pertsev, “Matrix stability and instability criteria for some systems of linear delay differential equations”, Sib. Èlektron. Mat. Izv., 16 (2019), 876–885
21.
N. V. Pertsev, B. Yu. Pichugin, K. K. Loginov, “Stochastic analog of the dynamic model of HIV-1 infection described by delay differential equations”, Sib. Zh. Ind. Mat., 22:1 (2019), 74–89; J. Appl. Industr. Math., 13:1 (2019), 103–117
N. V. Pertsev, B. Yu. Pichugin, A. N. Pichugina, “Application of M-matrices for the study of mathematical models of living systems”, Mat. Biolog. Bioinform., 13:Suppl. (2018), 104–131
N. V. Pertsev, B. Yu. Pichugin, A. N. Pichugina, “Application of M-matrices for the study of mathematical models of living systems”, Mat. Biolog. Bioinform., 13:1 (2018), 208–237
V. V. Malygina, M. V. Mulyukov, N. V. Pertsev, “On local asymptotic stability of a model of epidemic process”, Sib. Èlektron. Mat. Izv., 15 (2018), 1301–1310
25.
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”, Sibirsk. Mat. Zh., 59:1 (2018), 143–157; Siberian Math. J., 59:1 (2018), 113–125
N. V. Pertsev, B. Yu. Pichugin, A. N. Pichugina, “Investigation of solutions to one family of mathematical models of living systems”, Izv. Vyssh. Uchebn. Zaved. Mat., 2017, no. 9, 54–68; Russian Math. (Iz. VUZ), 61:9 (2017), 48–60
N. V. Pertsev, “Some properties of solutions to a family of integral equations arising in the models of living systems”, Sibirsk. Mat. Zh., 58:3 (2017), 673–685; Siberian Math. J., 58:3 (2017), 525–535
N. V. Pertsev, B. Yu. Pichugin, A. N. Pichugina, “The correctness of a family of integral and delay differential equations, used in models of living systems”, Sib. Èlektron. Mat. Izv., 13 (2016), 815–828
2015
29.
N. V. Pertsev, “Analysis of solutions to mathematical models of epidemic processes with common structural properties”, Sib. Zh. Ind. Mat., 18:2 (2015), 85–98
V. V. Malygina, M. V. Mulyukov, N. V. Pertsev, “On the local stability of a population dynamics model with delay”, Sib. Èlektron. Mat. Izv., 11 (2014), 951–957
N. V. Pertsev, B. Yu. Pichugin, A. N. Pichugina, “Analysis of the Asymptotic Behavior Solutions of Some Models of Epidemic Processes”, Mat. Biolog. 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”, Mat. Tr., 16:2 (2013), 111–141; Siberian Adv. Math., 24:4 (2014), 240–260
N. V. Pertsev, “Two-sided estimates for solutions to the Cauchy problem for Wazewski linear differential systems with delay”, Sibirsk. Mat. Zh., 54:6 (2013), 1368–1379; Siberian Math. J., 54:6 (2013), 1088–1097
N. V. Pertsev, G. E. Tsaregorodtseva, “Modeling population dynamics under the influence of harmful substances on the individual reproduction process”, Avtomat. i Telemekh., 2011, no. 1, 141–153; Autom. Remote Control, 72:1 (2011), 129–140
N. V. Pertsev, K. K. Loginov, “Stochastic model of dynamics of biological community in conditions of consumption by individuals of harmful food resources”, Mat. Biolog. Bioinform., 6:1 (2011), 1–13
N. V. Pertsev, B. Yu. Pichugin, K. K. Loginov, “Statistical modeling of the dynamics of populations affected by toxic pollutants”, Sib. Zh. Ind. Mat., 14:2 (2011), 84–94
V. Leonenko, N. V. Pertsev, “Efficiency analysis of the programs of exposure of individuals predisposed to colorectal cancer based on imitational modeling”, UBS, 35 (2011), 207–236
N. V. Pertsev, G. E. Tsaregorodtseva, “A mathematical model for the dynamics of a population affected by pollutants”, Sib. Zh. Ind. Mat., 13:1 (2010), 109–120; J. Appl. Industr. Math., 5:1 (2011), 94–103
N. V. Pertsev, B. Yu. Pichugin, “Индивидуум-ориентированная стохастическая модель распространения туберкулеза”, Sib. Zh. Ind. Mat., 12:2 (2009), 97–110; J. Appl. Industr. Math., 4:3 (2010), 359–370
R. O. Karelina, N. V. Pertsev, “Construction of two-sided estimates for solutions of some systems of differential equations with aftereffect”, Sib. Zh. Ind. Mat., 8:4 (2005), 60–72
N. V. Pertsev, A. N. Pichugina, B. Yu. Pichugin, “Behavior of solutions of a dissipative integral Lotka-Volterra model”, Sib. Zh. Ind. Mat., 6:2 (2003), 95–106
N. V. Pertsev, “Application of the monotone method and of $M$-matrices to the analysis of the behavior of solutions of some models of biological processes”, Sib. Zh. Ind. Mat., 5:4 (2002), 110–122
N. V. Pertsev, “Two-sided estimates for solutions of an integrodifferential equation that describes the hematogenic process”, Izv. Vyssh. Uchebn. Zaved. Mat., 2001, no. 6, 58–62; Russian Math. (Iz. VUZ), 45:6 (2001), 55–59
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. Uravn., 35:9 (1999), 1187–1193; Differ. Equ., 35:9 (1999), 1201–1207
N. V. Pertsev, “On bounded solutions of a class of systems of integral equations that arise in models of biological processes”, Differ. Uravn., 35:6 (1999), 831–836; Differ. Equ., 35:6 (1999), 835–840
N. V. Pertsev, “On the stability of the zero solution of a system of integrodifferential equations that arise in models of population dynamics”, Izv. Vyssh. Uchebn. Zaved. Mat., 1999, no. 8, 47–53; Russian Math. (Iz. VUZ), 43:8 (1999), 44–49
N. V. Pertsev, “On the asymptotic behavior of solutions of a system of linear differential equations with delay”, Izv. Vyssh. Uchebn. Zaved. Mat., 1996, no. 9, 48–52; Russian Math. (Iz. VUZ), 40:9 (1996), 45–49
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. Akad. Nauk SSSR, 297:1 (1987), 23–25; Dokl. Math., 36:3 (1988), 404–407
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