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Journal of Automation and Information Sciences
SJR: 0.275 SNIP: 0.59 CiteScore™: 0.8

ISSN Druckformat: 1064-2315
ISSN Online: 2163-9337

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Journal of Automation and Information Sciences

DOI: 10.1615/JAutomatInfScien.v45.i10.90
pages 75-82

Construction of Estimates of Solutions in the Model of Antitumor Immunity with Impulse Disturbances

Vasiliy P. Martsenyuk
Ternopol State I.Ya. Gorbachevskiy Medical University, Ukraine
O. A. Bagriy-Zayats
I.Ya. Horbachevsky Ternopol State Medical University


A model of antitumor immunity with impulse disturbances on the population of proliferating cells is proposed. Asymptotic estimates of solutions of the equations are obtained. Estimates are built on the bases of impulse differential inequalities for functions of the Lyapunov type.


  1. Martsenyuk V.P., Construction and study of the stability of the model of antitumor immunity.

  2. Martseniuk V.P, Andrushchak I.E., Bagrij-Zayats O.A., On the conditions of the asymptotic stability in the growth models of pathological formations based on the Richard dynamics.

  3. Marchuk G.I., Mathematical models in immunology.

  4. Haddad W.M., Chellaboina V.S., Nersesov S.G., Impulsive and hybrid dynamical systems: stability, dissipativity and control.

  5. Lakshmikantham V., Bainov D.D., Simeonov P.S., Theory of impulsive differential equations.

  6. Hale J., Theory of functional differential equations.

  7. Kato J., Yoshizawa Т., Remarks on global properties in limiting equations.

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