Super-twisting sliding mode control approach for tumor growth by immunotherapy

Abstract

Cancer is the second leading cause of death after heart disease in the world and the third leading cause of death after heart disease and accidents in Iran. In general, cancer is a disorder of the rate of proliferation and cell differentiation that can occur in any tissue of the body and at any age and by invading healthy tissues may exacerbate the disease and eventually cause death. In a word, one of the most commonly used treatments for cancer is the use of chemotherapy. The drugs of the aforementioned chemotherapy are transported through the blood to cancer cells and all parts of the body. In addition to cancer cells, these drugs also have a detrimental effect on healthy cells, which can be seen as side effects. It is to note that they are temporary and can stop at the end of treatment. The subject behind this research is to propose super-twisting sliding mode control approach without chattering for mathematical model of cancer by immunotherapy with the aim of stabilizing the closed-loop system, as long as determining the optimal drug dose is taken into consideration as the innovation of this study to conclude which controller has the better performance in the presence of uncertainties and disturbances.

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Abbreviations

\( \gamma \) :

Fixed and positive parameter in effective cell rotation

\( u\left( t \right) \) :

Effective cell external source rate

\( \tau_{g} \) :

Delay in interleukin concentration

\( V_{g} \) :

Cell distribution rate

\( V_{i} \) :

Interleukin concentration rate

\( K_{xgi} \) :

Interleukin-dependent tumor cell rate

\( T_{gh} \) :

Effective cell and tumor cell communication index

\( T_{igmax} \) :

The maximum rate of interleukin secretion in phase II

\( G_{b} \) :

Target mass index

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Correspondence to A H MAZINAN.

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AZARBAKHSH, G., MAZINAN, A.H. Super-twisting sliding mode control approach for tumor growth by immunotherapy. Sādhanā 45, 112 (2020). https://doi.org/10.1007/s12046-020-01348-8

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Keywords

  • Super-twisting sliding mode control approach
  • cancer treatment
  • tumor modeling
  • immunotherapy