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Numerical modelling in biosciences using delay differential equations. (English) Zbl 0969.65124
Summary: 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.

65R20 Numerical methods for integral equations
92B20 Neural networks for/in biological studies, artificial life and related topics
92C45 Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.)
92-08 Computational methods for problems pertaining to biology
92D25 Population dynamics (general)
45J05 Integro-ordinary differential equations
45G10 Other nonlinear integral equations
92D30 Epidemiology
Full Text: DOI
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