A family of models of angiogenesis and anti-angiogenesis anti-cancer therapy

Alberto D'Onofrio, Alberto Gandolfi

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we propose a class of models that describe the mutual interaction between tumour growth and the development of tumour vasculature and that generalize existing models. The study is mainly focused on the effect of a therapy that induces tumour vessel loss (anti-angiogenic therapy), with the aim of finding conditions that asymptotically guarantee the eradication of the disease under constant infusion or periodic administration of the drug. Furthermore, if tumour and/or vessel dynamics exhibit time delays, we derive conditions for the existence of Hopf bifurcations. The destabilizing effect of delays on achieving the tumour eradication is also investigated. Finally, global conditions for stability and eradication in the presence of delays are given for some particular cases.

Original languageEnglish
Pages (from-to)63-95
Number of pages33
JournalMathematical Medicine and Biology
Volume26
Issue number1
DOIs
Publication statusPublished - 2009

Keywords

  • Angiogenesis
  • Anti-angiogenesis
  • Delay differential equations
  • Stability
  • Tumour eradication

ASJC Scopus subject areas

  • Biochemistry, Genetics and Molecular Biology(all)
  • Environmental Science(all)
  • Immunology and Microbiology(all)
  • Applied Mathematics
  • Modelling and Simulation
  • Neuroscience(all)
  • Pharmacology

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