Numerical modelling in biosciences using delay differential equations

Gennadii A. Bocharov, Fathalla A. Rihan

Research output: Contribution to journalArticlepeer-review

243 Citations (Scopus)

Abstract

Our principal purposes here are (i) to consider, from the perspective of applied mathematics, models of phenomena in the biosciences that are based on delay differential equations and for which numerical approaches are a major tool in understanding their dynamics, (ii) to review the application of numerical techniques to investigate these models. We show that there are prima facie reasons for using such models: (i) they have a richer mathematical framework (compared with ordinary differential equations) for the analysis of biosystem dynamics, (ii) they display better consistency with the nature of certain biological processes and predictive results. We analyze both the qualitative and quantitative role that delays play in basic time-lag models proposed in population dynamics, epidemiology, physiology, immunology, neural networks and cell kinetics. We then indicate suitable computational techniques for the numerical treatment of mathematical problems emerging in the biosciences, comparing them with those implemented by the bio-modellers.

Original languageEnglish
Pages (from-to)183-199
Number of pages17
JournalJournal of Computational and Applied Mathematics
Volume125
Issue number1-2
DOIs
Publication statusPublished - Dec 15 2000
Externally publishedYes

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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