A fractional-order delay differential model with optimal control for cancer treatment based on synergy between anti-angiogenic and immune cell therapies

Nasser Sweilam, Fathalla Rihan, Seham AL-Mekhlafi

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

In this paper, we present an optimal control problem of fractional-order delay-differential model for cancer treatment based on the synergy between anti-angiogenic and immune cells therapies. The governed model consists of eighteen differential equations. A discrete time-delay is incorporated to represent the time required for the immune system to interact with the cancer cells, and fractional-order derivative is considered to reflect the memory and hereditary properties in the process. Two control variables for immunotherapy and anti-angiogenic therapy are considered to reduce the load of cancer cells. Necessary conditions that guarantee the existence and the uniqueness of the solution for the control problem have been considered. We approximate numerically the solution of the optimal control problem by solving the state system forward and adjoint system backward in time. Some numerical simulations are provided to validate the theoretical results.

Original languageEnglish
Pages (from-to)2403-2424
Number of pages22
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume13
Issue number9
DOIs
Publication statusPublished - Sep 2020

Keywords

  • Anti-angiogenic therapy
  • Cancer treatment
  • Delay differential equations
  • Fractional-calculus
  • Hamiltonian
  • Immunotherapy
  • Optimal control

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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