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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

A Cancer Model Study to See the Dynamical Effect of a Therapeutic Approach through Virus Injecting

Journal of Applied Nonlinear Dynamics 12(4) (2023) 739--756 | DOI:10.5890/JAND.2023.12.008

Aktar Saikh$^1$, Kalyan Das$^2$, Nurul Huda Gazi$^1$

$^1$ Department of Mathematics and Statistics, Aliah University, IIA/27, New Town, Kolkata-700160, India

$^2$ Department of Mathematics, National Institute of Food Technology Entrepreneurship and Management,

HSIIDC Industrial Estate, Kundli, Haryana 131028, India

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Abstract

A basic simple cancer model is studied to see the effectiveness of a therapeutic approach to control or reduce the cancer cells through a specific virus injecting into the patient's tumour site. Existence, uniqueness, positivity, persistency, boundedness of the system's solutions are established. The system's local and global behaviour about all possible equilibria are studied. Bifurcation analysis of the system is discussed as well. The basic reproduction number $\mathcal{R}_0$ is calculated using Next Generation Matrix method, which plays a significant role in the disease endemicity. We have analyzed the centre manifold near the tumour-free equilibrium point $E_0$, $\mathcal{R}_0=1$. For the proposed cancer model system, it is shown that there exists an optimal control of the virus replication rate. The characterization of the optimal control is explained as well. The optimality of the viral cytotoxicity is also studied. Numerical simulations are presented to validate the analytical findings. Finally, we conclude some epidemiological remarks made through analytical and numerical observations.

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