On an Impulsive Conformable M1 Oncolytic Virotherapy Neural Network Model: Stability of Sets Analysis

Gani Stamov, Ivanka Stamova () and Cvetelina Spirova
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Gani Stamov: Department of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USA
Ivanka Stamova: Department of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USA
Cvetelina Spirova: Department of Mathematics, Technical University of Sofia, 8800 Sliven, Bulgaria

Mathematics, 2025, vol. 13, issue 1, 1-22

Abstract: In this paper, the impulsive conformable calculus approach is applied to the introduction of an M 1 oncolytic virotherapy neural network model. The proposed model extends some existing mathematical models that describe the dynamics of the concentrations of normal cells, tumor cells, nutrients, M 1 viruses and cytotoxic T lymphocyte (CTL) cells to the impulsive conformable setting. The conformable concept allows for flexibility in the modeling approach, as well as avoiding the complexity of using classical fractional derivatives. The impulsive generalization supports the application of a suitable impulsive control therapy. Reaction–diffusion terms are also considered. We analyze the stable behavior of sets of states, which extend the investigations of the dynamics of separate equilibrium points. By applying the impulsive conformable Lyapunov function technique, sufficient conditions for the uniform global exponential stability of sets of states are established. An example is also presented to illustrate our results.

Keywords: oncolytic virotherapy; immune response; M 1 virus; conformable derivative; impulses; reaction–diffusion; stability of sets (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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