Russian version English version
Volume 8   Issue 1   Year 2013
Pertsev N.V., Pichugin B.Yu., Pichugina A.N.

Analysis of the Asymptotic Behavior Solutions of Some Models of Epidemic Processes

Mathematical Biology & Bioinformatics. 2013;8(1):21-48.

doi: 10.17537/2013.8.21.


  1. Anderson RM, May RM, Anderson B. Infectious Diseases of Humans: Dynamics and Control. Oxford University Press, USA; 1992. 768 p.
  2. Avilov KK, Romanyukha AA. Mathematical Models of Tuberculosis Extension and Control of It (review). Mathematical Biology and Bioinformatics. 2007;2(2):188–318.  doi: 10.17537/2007.2.188
  3. Nosova E. Models of Control and Spread of HIV-infection. Mathematical Biology and Bioinformatics. 2012;7(2):632–675. doi: 10.17537/2012.7.632
  4. Cooke K, York J. Some equations Modelling Growth Processes and Gonorhea Epidemics. Math. Biosc. 1973;16:75–101. doi: 10.1016/0025-5564(73)90046-1
  5. Busenberg S, Cooke K. The Effect of Integral Conditions in Certain Equations Modelling Epidemics and Population Growth. J. Math. Biol. 1980;10:13–32. doi: 10.1007/BF00276393
  6. Hethcote HW, Stech HW, van den Driessche P. Stability analisys for models of diseases without immunity. J. Math. Biol. 1981;13:185–198. doi: 10.1007/BF00275213
  7. Perelman MI, Marchuk GI, Borisov SE, Kazennykh BYa, Avilov KK, Karkach AS, Romanyukha AA. Tuberculosis epidemiology in Russia: the mathematical model and data analysis. Russ. J. Numer. Anal. Math. Modelling. 2004;19(4):305–314. doi: 10.1515/1569398041974905
  8. Avilov KK, Romanyukha AA. Mathematical modeling of tuberculosis propagation and patient detection. Automation and Remote Control. 2007;68(9):1604-1617. doi: 10.1134/S0005117907090159
  9. Melnichenko AO, Romanyukha AA. A model of tuberculosis epidemiology: estimation of parameters and analysis of factors influencing the dynamics of an epidemic process. Russ. J. Numer. Anal. Math. Modelling. 2008;23(1):1–13. doi: 10.1515/rnam.2008.004
  10. Romaniukha AA, Nosova EA. Upravlenie bol'shimi sistemami (Large-Scale System Control). 2011;34:227-253 (in Russ.).
  11. Kolmanovskii VB, Nosov VR. Ustoichivost' i periodicheskie rezhimy reguliruemykh sistem s posledeistviem (Stability and periodic regimes of controlled systems with aftereffect) . Moscow; 1981. 448 p. (in Russ.).
  12. Hale JK. The theory of functional differential equations. Springer-Verlag; 1977. 365 p. doi: 10.1007/978-1-4612-9892-2
  13. Krasnoselʹskiĭ MA. Positive solutions of operator equations. P. Noordhoff; 1964.
  14. Introduction to the Theory and Application of Differential Equations with Deviating Arguments. Eds. El'sgol'ts LE and Norkin SB. 1973. (Mathematics in Science and Engineering. V. 105).
  15. Demidovich BP. Lektsii po matematicheskoi teorii ustoichivosti (Lectures on the mathematical theory of stability). Moscow; 1967. 472 p. (in Russ.)
  16. Barbashin EA. Introduction to the theory of stability. Wolters-Noordhoff; 970. 223 p.
  17. Bellman R. Introduction to Matrix Analysis. 2 edition. Society for Industrial and Applied Mathematics; 1987. 430 p. (Classics in Applied Mathematics). Gantmacher F. Theory of matrices. AMS Chelsea publishing; 1959.
  18. Voevodin VV, Kuznetsov YuA. Matritsy i vychisleniia (Matrices and computing). Moscow; 1984. 320 p. (in Russ.).
  19. Berman A, Plemmons RJ. Nonnegative matrices in the mathematical sciences. New York: Academic Press; 1979. 340 p.
  20. Obolenskii AYu. Stability of solutions of autonomous Wazewski systems with delayed action. Ukrainian Mathematical Journal. 1983;35(5):486-492. doi: 10.1007/BF01061640
Table of Contents Original Article
Math. Biol. Bioinf.
doi: 10.17537/2013.8.21
published in Russian

Abstract (rus.)
Abstract (eng.)
Full text (rus., pdf)


  Copyright IMPB RAS © 2005-2022