Stability analysis of a targeted chemotherapy-cancer model

Anusmita Das; Kaushik Dehingia; Nabajit Ray; Hemanta Kumar Sarmah; Anusmita Das; Kaushik Dehingia; Nabajit Ray; Hemanta Kumar Sarmah

doi:10.3934/mmc.2023011

Mathematical Modelling and Control

2023, Volume 3, Issue 2: 116-126. doi: 10.3934/mmc.2023011

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Research article

Stability analysis of a targeted chemotherapy-cancer model

1.
Department of Mathematics, Udalguri College, Udalguri 784509, Assam, India
2.
Department of Mathematics, Sonari College, Sonari 785690, Assam, India
3.
Department of Mathematics, S.B. Deorah College, Guwahati 781007, Assam, India
4.
Department of Mathematics, Gauhati University, Guwahati 781014, Assam, India

Received: 05 November 2022 Revised: 13 February 2023 Accepted: 23 February 2023 Published: 05 June 2023

This study addresses a modified mathematical model of tumor growth with targeted chemotherapy consisting of effector cells, tumor cells, and normal cells. To investigate the dynamics of the model, local and global stability analyses have been performed at the equilibrium points of the model. It is found that the tumor-free steady state is globally asymptotically stable under certain conditions, which suggests that the prescribed treatment can eradicate tumor cells from the body for a threshold value of tumor growth rate. The main result of this study is that if the tumor growth rate is tiny, it is possible to eradicate the tumor from the body using a smaller amount of targeted chemotherapy drugs with less harm to the other healthy cells. If not, it requires a high dose of targeted chemotherapy drugs, which can increase the side effects of the drugs. Numerical simulations have been performed to verify our analytical results.
- cancer,
- targeted chemotherapy,
- stability,
- numerical simulation
Citation: Anusmita Das, Kaushik Dehingia, Nabajit Ray, Hemanta Kumar Sarmah. Stability analysis of a targeted chemotherapy-cancer model[J]. Mathematical Modelling and Control, 2023, 3(2): 116-126. doi: 10.3934/mmc.2023011

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Abstract

This study addresses a modified mathematical model of tumor growth with targeted chemotherapy consisting of effector cells, tumor cells, and normal cells. To investigate the dynamics of the model, local and global stability analyses have been performed at the equilibrium points of the model. It is found that the tumor-free steady state is globally asymptotically stable under certain conditions, which suggests that the prescribed treatment can eradicate tumor cells from the body for a threshold value of tumor growth rate. The main result of this study is that if the tumor growth rate is tiny, it is possible to eradicate the tumor from the body using a smaller amount of targeted chemotherapy drugs with less harm to the other healthy cells. If not, it requires a high dose of targeted chemotherapy drugs, which can increase the side effects of the drugs. Numerical simulations have been performed to verify our analytical results.

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