Mathematical model of brain tumour growth with drug resistance

José Trobia, Kun Tian, Antonio Marcos Batista* (Corresponding Author), Celso Grebogi, Hai-Peng Ren, Moises Souza Santos, Paulo Ricardo Protachevicz, Fernando da Silva Borges, José Danilo Szezech Jr, Ricardo Luiz Viana, Iberê Luiz Caldas, Kelly Cristiane Iarosz* (Corresponding Author)

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)
44 Downloads (Pure)


In this research article, we propose a model with glioma drug resistance for gliomas with glia-neuron interactions and chemotherapy treatment.
We consider continuous and pulsed chemotherapy to destroy glioma cells without harming a large number of neurons and we computed the values of the infusion of chemotherapy agents in which the glioma is suppressed and a minimum number of neurons is lost, without neurogenesis.
The main contribution of this work is the insertion of a new differential equation to the model formulated in 2015 by Iarosz and collaborators. The new equation extend the mathematical model of brain tumour growth and and enables the study of sensitive and resistant glioma cells.
Original languageEnglish
Article number106013
Number of pages10
JournalCommunications in Nonlinear Science & Numerical Simulation
Early online date31 Aug 2021
Publication statusPublished - 1 Dec 2021

Bibliographical note

We wish to acknowledge the support: Araucária Fundation, National Council for Scientific and Technological Development (CNPq, 302665/2017-0 and 407299/2018-1), Coordination for the Improvement of Higher Education Personnel (CAPES), and São Paulo Research Foundation (Processes 2015/07311-7, 2017/18977-1, 2018/03211-6, 2020/04624-2). The authors would like to thank the 105 Group Science ( for the fruitful discussions.


  • brain
  • tumor
  • chemotherapy
  • drug resistance
  • glia-neuron interaction


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