https://doi.org/10.1140/epjp/s13360-024-05004-6
Regular Article
Modeling the dynamics of mixed immunotherapy and chemotherapy for the treatment of immunogenic tumor
1
Department of Mathematics, Jadavpur University, 700032, Kolkata, India
2
Department of Mathematics, Presidency University, 86/1 College Street, 700073, Kolkata, India
c
subhas.maths@presiuniv.ac.in
Received:
13
December
2023
Accepted:
13
February
2024
Published online:
7
March
2024
We investigate a mathematical model that delineates the nonlinear dynamics of tumor-immune interplay by considering the roles of immunotherapy and chemotherapy. The proposed model explores a system of coupled nonlinear ordinary differential equations (ODEs), involving tumor cells, cytotoxic T-lymphocytes (CD8+T cells), macrophages, dendritic cells, regulatory T-cells (Tregs), IL-10, TGF-
, IL-12, IFN-
and the concentration of chemotherapeutic drug. We use optimal control theory to understand the dynamics under what conditions the immune system can eradicate tumor cells. The control problem is solved with an objective functional that minimizes the tumor cell population and maximizes the immune components. The basic properties of optimal control theory are established through the boundedness of solutions for each state variable. Our optimal control theory is characterized by coupling the state variables with costates. Additionally, our study investigates the uniqueness property of the optimal control problem within a small time window. Subsequently, we explored the methods employed to estimate the system parameters. Finally, we demonstrate numerically that the optimal control strategy minimizes the burden of tumor cells and maximizes immune cell populations under different scenarios. Moreover, we provide corresponding biological implications.
Copyright comment 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.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. 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.
