Numerical bifurcation analysis of immunological models with time delays

Authors:
Tatyana Luzyanina;Dirk Roose;Gennady Bocharov
Affiliations:
Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, B-3001 Heverlee-Leuven, Belgium;Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, B-3001 Heverlee-Leuven, Belgium;Institute of Numerical Mathematics, RAS, Gubkina str. 8, Moscow, 119991, Russia and Department of Infectious Disease Epidemiology, Imperial College of Science, Technology and Medicine, St. Mary's ...
Venue:
Journal of Computational and Applied Mathematics - Special issue: Mathematics applied to immunology
Year:
2005

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Abstract

In recent years, a large number of mathematical models that are described by delay differential equations (DDEs) have appeared in the life sciences. To analyze the models' dynamics, numerical methods are necessary, since analytical studies can only give limited results. In turn, the availability of efficient numerical methods and software packages encourages the use of time delays in mathematical modelling, which may lead to more realistic models. We outline recently developed numerical methods for bifurcation analysis of DDEs and illustrate the use of these methods in the analysis of a mathematical model of human hepatitis B virus infection.