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Fractional Tumour-Immune Model with Drug Resistance

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Abstract

Cancer is a group of diseases in which cells grow uncontrollably and can spread into other tissues. Various studies consider the interactions between cancer cells and the immune system as well as different types of treatment. Mathematical models have been used to study the growth of cancerous cells. We study a fractional order model that describes some aspects of the interactions among host, effector immune, and cancer cells. A drug treatment is considered to analyse the cancerous cells proliferation. Due to the chemotherapy, we split the fractional equation of the cancerous cells into drug sensitivity and resistance. We show that not only the chemotherapy but also the drug resistance plays an important role in the growth rate of cancer cells.

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Acknowledgements

This work was possible by partial financial support from the following Brazilian government agencies: CNPq, CAPES, Fundação Araucária, and Fundação de Amparo à Pesquisa do Estado de São Paulo. We would like to thank www.105groupscience.com.

Funding

I.L.C. received financial support from Fundação de Amparo à Pesquisa do Estado de São Paulo, processo FAPESP 2018/03211-6. E.C.G. received financial support from Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 88881.846051/2023-01.

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Author notes

  1. All authors contributed equally to this work.

Authors and Affiliations

  1. Graduate Program in Science, State University of Ponta Grossa, 84030-900, Ponta Grossa, PR, Brazil

    Ana P. S. Koltun, Antonio M. Batista, Ervin K. Lenzi, Fernando S. Borges, Kelly C. Iarosz & Enrique C. Gabrick

  2. Department of Mathematics and Statistics, State University of Ponta Grossa, 84030-900, Ponta Grossa, PR, Brazil

    José Trobia & Antonio M. Batista

  3. Department of Physics, State University of Ponta Grossa, 84030-900, Ponta Grossa, PR, Brazil

    Ervin K. Lenzi

  4. Municipal Secretary of Education of Ponta Grossa, Ponta Grossa, PR, Brazil

    Moises S. Santos

  5. Department of Physiology and Pharmacology, State University of New York Downstate Health Sciences University, Brooklyn, NY, USA

    Fernando S. Borges

  6. Center for Mathematics, Computation, and Cognition, Federal University of ABC, São Paulo, Brazil

    Fernando S. Borges

  7. University Center UNIFATEB, 84266-010, PR, Telêmaco Borba, Brazil

    Kelly C. Iarosz

  8. Physics Intitute, University of São Paulo, 05508-090, São Paulo, SP, Brazil

    Iberê L. Caldas

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  1. Ana P. S. Koltun
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All authors discussed the results and contributed to the final manuscript.

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Correspondence to Ana P. S. Koltun.

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Koltun, A.P.S., Trobia, J., Batista, A.M. et al. Fractional Tumour-Immune Model with Drug Resistance. Braz J Phys 54, 41 (2024). https://doi.org/10.1007/s13538-024-01417-x

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