Voir la notice de l'article provenant de la source Math-Net.Ru
@article{SEMR_2018_15_a104, author = {V. V. Malygina and M. V. Mulyukov and N. V. Pertsev}, title = {On local asymptotic stability of a model of epidemic process}, journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a}, pages = {1301--1310}, publisher = {mathdoc}, volume = {15}, year = {2018}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a104/} }
TY - JOUR AU - V. V. Malygina AU - M. V. Mulyukov AU - N. V. Pertsev TI - On local asymptotic stability of a model of epidemic process JO - Sibirskie èlektronnye matematičeskie izvestiâ PY - 2018 SP - 1301 EP - 1310 VL - 15 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SEMR_2018_15_a104/ LA - ru ID - SEMR_2018_15_a104 ER -
%0 Journal Article %A V. V. Malygina %A M. V. Mulyukov %A N. V. Pertsev %T On local asymptotic stability of a model of epidemic process %J Sibirskie èlektronnye matematičeskie izvestiâ %D 2018 %P 1301-1310 %V 15 %I mathdoc %U http://geodesic.mathdoc.fr/item/SEMR_2018_15_a104/ %G ru %F SEMR_2018_15_a104
V. V. Malygina; M. V. Mulyukov; N. V. Pertsev. On local asymptotic stability of a model of epidemic process. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1301-1310. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a104/
[1] G. Huang, Y. Takeuchi, “Global analysis on delay epidemiological dynamic models with nonlinear incidence”, J. Math. Biol., 63:1 (2011), 125–139 | DOI | MR | Zbl
[2] Y. Muroya, T. Kuniya, J. Wang, “Stability analysis of a delayed multi-group SIS epidemic model with nonlinear incidence rates and patch structure”, J. Math. Anal. Appl., 425:1 (2015), 415–439 | DOI | MR | Zbl
[3] D. Okuonghae, “A note on some qualitative properties of a tuberculosis differential equation model with a time delay”, Differ. Equ. Dyn. Syst., 23:2 (2015), 181–194 | DOI | MR | Zbl
[4] M. A. Skvortsova, “Asymptotic properties of solutions to a system describing the spread of avian influenza”, Siberian Electronic Mathematical Reports, 13 (2016), 782–798 | MR | Zbl
[5] L. M. Taylor, T. W. Carr, “An SIR epidemic model with partial temporary immunity modeled with delay”, J. Math. Biol., 59:6 (2009), 841–880 | DOI | MR | Zbl
[6] L. Wang, R. Xu, G. Feng, “Modelling and analysis of an eco-epidemiological model with time delay and stage structure”, J. Appl. Math. Comput., 50:1–2 (2016), 175–197 | DOI | MR | Zbl
[7] Y. Xiao, L. Chen, “An SIS epidemic model with stage structure and a delay”, Acta Mathematicae Applicatae Sinica, English Series, 18:4 (2002), 607–618 | DOI | MR | Zbl
[8] Y. Yuan, J. Belair, “Threshold dynamics in an SEIRS model with latency and temporary immunity”, J. Math. Biol., 69:4 (2014), 875–904 | DOI | MR | Zbl
[9] N. V. Pertsev, B. Yu. Pichugin, A. N. Pichugina, “Investigation of an asymptotic behavior of solutions of some epidemic processes models”, Mathematical Biology and Bioinformatics, 8:1 (2013), 21–48 | DOI
[10] N. V. Azbelev, V. P. Maksimov, L. F. Rakhmatullina, Introduction to the Theory of Linear Functional Differential Equations, World Federation Publishers Company, Atlanta, 1995 | MR | MR | Zbl | Zbl
[11] N. V. Azbelev, P. M. Simonov, Stability of Differential Equations with Aftereffect, Taylor, London, 2002 | MR
[12] A. A. Andronov, A. G. Mayer, “The simplest linear systems with delay”, Automation and Remote Control, 7:2–3 (1946), 95–106 | MR | Zbl
[13] A. Yu. Obolenskiy, “On stability of solutions of Vazewski autonomous systems with delay”, Ukrainian Mathematical Journal, 35 (1983), 574–579 | MR
[14] R. Volz, “Stability Conditions for Systems of Linear Nonautonomous Delay Differential Equations”, J. Math. Anal. Appl., 120:2 (1986), 584–595 | DOI | MR | Zbl
[15] V. B. Kolmanovskiy, V. R. Nosov, Stability and periodic modes of a controlled systems with aftereffect, Nauka, M., 1981 | MR
[16] T. L. Sabatulina, V. V. Malygina, “On stability of a differential equation with bounded aftereffect”, Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 4 (2014), 25–41 | MR | Zbl
[17] R. Bellman, K. L. Cooke, Differential-Difference Equations, Mir, M., 1967 | MR | Zbl
[18] M. V. Mulyukov, “Stability of a linear differential equation with double delay”, Proceedings of VIII International Conference “Modern Problems of Applied Mathematics, Control Theory and Computer Science (AMCTCS-2018)” (Voronezh, Russia, 2015), 258–260
[19] M. V. Mulyukov, “The structure of D-decomposition regions for two-parameter characteristic equations of systems with delay”, Functional Differential Equations: Theory and Applications, Perm National Research Polytechnic University, Perm, 2018, 180–200
[20] T. Luzyanina, J. Sieber, K. Engelborghs, G. Samaey, D. Roose, “Numerical bifurcation analysis of mathematical models with time delays with the package DDE-BIFTOOL”, Mathematical Biology and Bioinformatics, 12:2 (2017), 496–520 | DOI