https://doi.org/10.1140/epjs/s11734-023-00929-y
Regular Article
Chaotic dynamics in a non-linear tumor-immune model with Caputo–Fabrizio fractional operator
1
Department of Mathematics, University of Malakand, Dir(L), Chakdara, Khyber Pakhtunkhwa, Pakistan
2
Department of Sciences and Technology, Ranyah University College, Taif University, P.O. Box 11099, 21944, Taif, Saudi Arabia
3
Institute of Energy Infrastructure (IEI), Department of Civil Engineering, College of Engineering, Universiti Tenaga Nasional (UNITEN), Putrajaya Campus, Jalan IKRAM-UNITEN, 43000, Kajang, Selangor, Malaysia
Received:
30
March
2023
Accepted:
2
July
2023
Published online:
22
August
2023
In this article, we investigate a tumor-immune and antigen-presenting cells population in the form of a mathematical model. To achieve greater accuracy in understanding the spread of tumor and immune cell populations, we apply the Caputo–Fabrizio (CF) fractional-order derivative. The fixed-point theorems are employed to analyze the uniqueness and existence of the model. The Laplace transform along with the Adomian decomposition approach is used to construct an algorithm for a semi-analytical solution under the CF fractional derivative. The chaotic dynamics of the cancer-immune model are confirmed by the Lyapunov exponents. The article examines how different vaccination protocols can affect tumor dormancy and recurrence. Furthermore, we offer a description for why adoptive immunotherapy techniques may potentially increase tumor growth rather than suppress it.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
