Targeting the quiescent cells in cancer chemotherapy treatment: Is it enough?

Abdessamad Tridane, Radouane Yafia, M. A. Aziz-Alaoui

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


In this work, we develop a mathematical model to study the effect of drug on the development of cancer including the quiescent compartment. The model is governed by a system of delay differential equations where the delay represents the time that the cancer cell take to proliferate. Our analytical study of the stability shows that by considering the time delay as a parameter of bifurcation, it is possible to have stability switch and oscillations through a Hopf bifurcation. Moreover, by introducing the drug intervention term, the critical delay value increases. This indicates that the system can tolerate a longer delay before oscillations start. In the end, we present some numerical simulations illustrating our theoretical results.

Original languageEnglish
Pages (from-to)4844-4858
Number of pages15
JournalApplied Mathematical Modelling
Issue number7-8
Publication statusPublished - Apr 1 2016


  • Chemotherapy
  • Delayed differential equations
  • Hopf bifurcation
  • Quiescent cells
  • Stability

ASJC Scopus subject areas

  • Modelling and Simulation
  • Applied Mathematics


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