Modeling and optimal control of cancer-immune system

Fathalla A. Rihan, Nouran F. Rihan

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Citation (Scopus)


In this chapter, we present a simple mathematical model of tumor-immune interactions in presence of chemotherapy treatment. The model is governed by a system of delay differential equations with optimal control variables. The control variables are included to justify the best treatment strategy with minimum side effects by reducing the production of new tumor cells and keeping the number of normal cells above the average of its carrying capacity. The numerical simulations show that the optimal treatment strategy reduces the load of tumor cells and increases the effector cells after just a few days of therapy.

Original languageEnglish
Title of host publicationControl Theory in Biomedical Engineering
Subtitle of host publicationApplications in Physiology and Medical Robotics
Number of pages22
ISBN (Electronic)9780128213506
Publication statusPublished - Jan 1 2020


  • 37N25
  • 37N35
  • 92C50
  • Chemotherapy
  • DDEs
  • Dynamical systems in control 34K28
  • Hamiltonian
  • Immune system
  • Mathematical modeling
  • Medical applications of mathematical biology 93A30
  • Optimal control
  • Time-lags

ASJC Scopus subject areas

  • General Agricultural and Biological Sciences
  • General Biochemistry,Genetics and Molecular Biology


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