Optimal control of effector-tumor-normal cells dynamics in presence of adoptive immunotherapy

Anusmita Das; Kaushik Dehingia; Hemanta Kumar Sharmah; Choonkil Park; Jung Rye Lee; Khadijeh Sadri; Kamyar Hosseini; Soheil Salahshour; Anusmita Das; Kaushik Dehingia; Hemanta Kumar Sharmah; Choonkil Park; Jung Rye Lee; Khadijeh Sadri; Kamyar Hosseini; Soheil Salahshour

doi:10.3934/math.2021570

AIMS Mathematics

2021, Volume 6, Issue 9: 9813-9834. doi: 10.3934/math.2021570

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Research article

Optimal control of effector-tumor-normal cells dynamics in presence of adoptive immunotherapy

1.
Department of Mathematics, Gauhati University, Guwahati 781014, Assam, India
2.
Research Institute for Natural Sciences, Hanyang University, Seoul 04763, South Korea
3.
Department of Data Science, Daejin University, Kyunngi 11159, South Korea
4.
Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran
5.
Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey

Received: 31 March 2021 Accepted: 16 June 2021 Published: 29 June 2021
MSC : 34L99, 65L06

Interactive dynamics between effector-tumor-normal cells in a mathematical model related to the growth of cancer in presence of immunotherapy has been discussed in the present paper. Adoptive immunotherapy has been added to the original model proposed by De Pillis et al. ^[1]. This has been done to get rid of the tumor cells. Different dynamical behaviours of the modified systems have been studied. The existence of the solution and global stability conditions of the healthy equilibrium point is addressed. Corresponding optimal control problem has been formulated to find the best possible way of administration of adoptive immunotherapy by which cancer cells can be eradicated without putting the patient at any health-related risk. To achieve this purpose, the quadratic control principle has been adopted. The dynamical behaviour of the effector-tumor-normal cells model with control is also numerically verified and demonstrated. Through numerical simulations, it is formally shown that the optimal regimens eradicate the tumor load in less time without putting the patientso health at any risk.
- mathematical model of cancer,
- adoptive immunotherapy,
- stability analysis,
- optimal control problem,
- quadratic control principle
Citation: Anusmita Das, Kaushik Dehingia, Hemanta Kumar Sharmah, Choonkil Park, Jung Rye Lee, Khadijeh Sadri, Kamyar Hosseini, Soheil Salahshour. Optimal control of effector-tumor-normal cells dynamics in presence of adoptive immunotherapy[J]. AIMS Mathematics, 2021, 6(9): 9813-9834. doi: 10.3934/math.2021570

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Abstract

Interactive dynamics between effector-tumor-normal cells in a mathematical model related to the growth of cancer in presence of immunotherapy has been discussed in the present paper. Adoptive immunotherapy has been added to the original model proposed by De Pillis et al. ^[1]. This has been done to get rid of the tumor cells. Different dynamical behaviours of the modified systems have been studied. The existence of the solution and global stability conditions of the healthy equilibrium point is addressed. Corresponding optimal control problem has been formulated to find the best possible way of administration of adoptive immunotherapy by which cancer cells can be eradicated without putting the patient at any health-related risk. To achieve this purpose, the quadratic control principle has been adopted. The dynamical behaviour of the effector-tumor-normal cells model with control is also numerically verified and demonstrated. Through numerical simulations, it is formally shown that the optimal regimens eradicate the tumor load in less time without putting the patientso health at any risk.

References

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