The tracking of derivative discontinuities in systems of delay-differential equations
Selected papers from the international conference on Numerical solution of Volterra and delay equations
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Pitfalls in Parameter Estimation for Delay Differential Equations
SIAM Journal on Scientific Computing
The nature of mathematical modeling
The nature of mathematical modeling
Numerical modelling in biosciences using delay differential equations
Journal of Computational and Applied Mathematics - Special issue on numerical anaylsis 2000 Vol. VI: Ordinary differential equations and integral equations
Retarded differential equations
Journal of Computational and Applied Mathematics - Special issue on numerical anaylsis 2000 Vol. VI: Ordinary differential equations and integral equations
Lancelot: A FORTRAN Package for Large-Scale Nonlinear Optimization (Release A)
Lancelot: A FORTRAN Package for Large-Scale Nonlinear Optimization (Release A)
Tutorial on maximum likelihood estimation
Journal of Mathematical Psychology
Applied Numerical Mathematics
Discontinuous solutions of neutral delay differential equations
Applied Numerical Mathematics
Parameter Estimation Using Metaheuristics in Systems Biology: A Comprehensive Review
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Proceedings of the 15th annual conference on Genetic and evolutionary computation
Mathematics and Computers in Simulation
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One of the significant challenges in biomathematics (and other areas of science) is to formulate meaningful mathematical models. Our problem is to decide on a parametrized model which is, in some sense, most likely to represent the information in a set of observed data. In this paper, we illustrate the computational implementation of an information-theoretic approach (associated with a maximum likelihood treatment) to modelling in immunology. The approach is illustrated by modelling LCMV infection using a family of models based on systems of ordinary differential and delay differential equations. The models (which use parameters that have a scientific interpretation) are chosen to fit data arising from experimental studies of virus-cytotoxic T lymphocyte kinetics; the parametrized models that result are arranged in a hierarchy by the computation of Akaike indices. The practical illustration is used to convey more general insight. Because the mathematical equations that comprise the models are solved numerically, the accuracy in the computation has a bearing on the outcome, and we address this and other practical details in our discussion.