Skip to main content
SpringerLink
Log in

Estimating the solutions in the model of antitumor immunity with impulsive disturbances

  • Published:
Cybernetics and Systems Analysis Aims and scope

Abstract

The authors propose a model of antitumor immunity with impulsive disturbances with respect to the population of proliferating cells. The asymptotic estimates are obtained for solutions of the equations. The estimates are based on impulsive differential inequalities for Lyapunov-type functions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V. P. Martsenyuk, “Construction and study of stability of an antitumoral immunity model,” Cybern. Syst. Analysis, 40, No. 5, 778–783 (2004).

    Article  MathSciNet  MATH  Google Scholar 

  2. A. K. Laird, “Dynamics of tumor growth,” Br J. of Cancer, 18, 490–502 (1964).

    Article  Google Scholar 

  3. G. I. Marchuk, Mathematical Models in Immunology [in Russian], Nauka, Moscow (1980).

    Google Scholar 

  4. W. M. Haddad, V. S. Chellaboina, and S. G. Nersesov, Impulsive and Hybrid Dynamical Systems: Stability, Dissipativity and Control, Princeton Univ. Press, Princeton (2008).

    Google Scholar 

  5. V. Lakshmikantham, D. D. Bainov, and P. S. Simeonov, Theory of Impulsive Differential Equations, World Sci. Publ. Co., Singapore (1989).

    MATH  Google Scholar 

  6. J. Hale, Theory of Functional Differential Equations, Springer-Verlag, New York–Heidelberg–Berlin (1977).

  7. J. Kato and T. Yoshizawa, “Remarks on global properties in limiting equations,” Funkcialaj Ekvacioj, 24, 363–371 (1981).

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. I. Ya. Gorbachevskii State Medical University, Ternopil, Ukraine

    V. P. Martsenyuk & I. S. Gvozdetska

  2. National Technical University, Lutsk, Ukraine

    I. Ye. Andruschchak

Authors
  1. V. P. Martsenyuk
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. Ye. Andruschchak
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. I. S. Gvozdetska
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. P. Martsenyuk.

Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 2, March–April, 2012, pp. 50–54.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Martsenyuk, V.P., Andruschchak, I.Y. & Gvozdetska, I.S. Estimating the solutions in the model of antitumor immunity with impulsive disturbances. Cybern Syst Anal 48, 200–204 (2012). https://doi.org/10.1007/s10559-012-9398-7

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10559-012-9398-7

Keywords

Search

Navigation