On an Impulsive Conformable M1 Oncolytic Virotherapy Neural Network Model: Stability of Sets Analysis
In this paper, the impulsive conformable calculus approach is applied to the introduction of an <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>M</mi><mn>1</mn></mrow><...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-01-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/1/141 |
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| Summary: | In this paper, the impulsive conformable calculus approach is applied to the introduction of an <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>M</mi><mn>1</mn></mrow></semantics></math></inline-formula> 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, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>M</mi><mn>1</mn></mrow></semantics></math></inline-formula> 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. |
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| ISSN: | 2227-7390 |