Abstract
Modeling the dynamics of infectious diseases, illicit drug initiation, or other systems, where the age of an individual or the duration of being in a specific state is essential, leads to a generalized form of the McKendrick equations, i.e., a system of first-order partial differential equations in the time-age space. Typically such models include age-specific feedback components which are represented by integral terms in the right hand side of the equation. This paper presents the general framework of such optimal control models, the corresponding necessary optimality conditions and two different approaches for numerical solution methods.
This work was partly financed by the Austrian Science Foundation under contract No. 14060-OEK and by the Austrian Science and Research Liaison Office Sofia.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Almeder, C., Caulkins, J.P., Feichtinger, G., Tragler, G.: An age-structured single-state drug initiation model — cycles of drug epidemics and optimal prevention programs, Research Report 249, Department of Operations Research and Systems Theory, Vienna University of Technology, Vienna (2000) (forthcoming in Social and Economic Planning Sciences)
Ascher, U., Christiansen, J., Russel, R.D.: Collocation software for boundary value odes. ACM Trans. Math. Software 7, 209–222 (1981)
Feichtinger, G., Hartl, R.F., Kort, P.M., Veliov, V.M.: Dynamic investment behavior taking into account aging of the capital, CentER Discussion Paper, No. 2001-13, Tilburg University (2001)
Feichtinger, G., Tragler, G., Veliov, V.M.: Optimality conditions for age-structured control systems. J. Math. Anal. Appl. (forthcoming)
Haurie, A., Sethi, S., Hartl, R.: Optimal control of an age-structured population model with applications to social services planning. Large Scale Systems 6, 133–158 (1984)
Iannelli, M., Milner, F.A., Pugliese, A.: Analytical and numerical results for the age-structured S-I-S epidemic model with mixed inter-intracohort transmission. SIAM J. Math. Anal. 23(3), 662–688 (1992)
Keyfitz, B.L., Keyfitz, N.: The McKendrick partial differential equation and its uses in epidomology and population studies. Math. Comput. Modelling 26(6), 1–9 (1997)
Schiesser, W.E.: The Numerical Method of Lines. Academic Press, London (1991)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Almeder, C. (2004). Solution Methods for Age-Structured Optimal Control Models with Feedback. In: Lirkov, I., Margenov, S., Waśniewski, J., Yalamov, P. (eds) Large-Scale Scientific Computing. LSSC 2003. Lecture Notes in Computer Science, vol 2907. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24588-9_21
Download citation
DOI: https://doi.org/10.1007/978-3-540-24588-9_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-21090-0
Online ISBN: 978-3-540-24588-9
eBook Packages: Springer Book Archive