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Zbl 0969.65124
Bocharov, Gennadii A.; Rihan, Fathalla A.
Numerical modelling in biosciences using delay differential equations. (English)
[J] J. Comput. Appl. Math. 125, No.1-2, 183-199 (2000). ISSN 0377-0427

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.

MSC 2000:: *65R20 Integral equations (numerical methods)
92B20 General theory of neural networks
92C45 Kinetics in biochemical problems
92-08 Computational methods (appl. to natural sciences)
92D25 Population dynamics
45J05 Integro-ordinary differential equations
45G10 Nonsingular nonlinear integral equations
92D30 Epidemiology

Keywords: nonlinear integro-differential equations; biological systems; numerical modelling; parameter estimation; retarded functional differential equations; delay differential equations; biosystem dynamics; population dynamics; epidemiology; physiology; immunology; neural networks; cell kinetics

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Zentralblatt MATH Berlin [Germany]