A time delay model of tumour-immune system interactions: Global dynamics, parameter estimation, sensitivity analysis

F. A. Rihan, D. H. Abdel Rahman, S. Lakshmanan, A. S. Alkhajeh

Research output: Contribution to journalArticlepeer-review

77 Citations (Scopus)

Abstract

Recently, a large number of mathematical models that are described by delay differential equations (DDEs) have appeared in the life sciences. In this paper, we present a delay differential model to describe the interactions between the effector and tumour cells. The existence of the possible steady states and their local stability and change of stability via Hopf bifurcation are theoretically and numerically investigated. Parameter estimation problem for given real observations, using least squares approach, is studied. The global stability and sensitivity analysis are also numerically proved for the model. The stability and periodicity of the solutions may depend on the time-lag parameter. The model is qualitatively consistent with the experimental observations of immune-induced tumour dormancy. The model also predicts dormancy as a transient period of growth which necessarily results in either tumour elimination or tumour escape.

Original languageEnglish
Pages (from-to)606-623
Number of pages18
JournalApplied Mathematics and Computation
Volume232
DOIs
Publication statusPublished - Apr 1 2014

Keywords

  • DDEs
  • Hopf bifurcation
  • Immune cells
  • Parameter estimation
  • Sensitivity
  • Stability
  • Tumour cells

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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