Abstract
We employ recent results on robust control of uncertain dynamical systems to deduce a screening policy for use by a public health authority in the control of an infectious disease such as gonorrhea.
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
Corless, M.; Leitmann, G.: Bounded controllers for robust exponential convergence, Journal of Optimization Theory and Applications, Vol. 76, pp. 1–12, 1993.
Corless M.; Leitmann, G.: Componentwise bounded controllers for robust exponential convergence, Proceedings of the Variable Structure and Lyapunov Theory Workshop, Sept. 7–9, 1994, Benevento, Italy, pp. 64–69.
Lee, C. S.; Leitmann, G.: A bounded harvest strategy for an ecological system in the presence of uncertain disturbances, Proceedings of the International Workshop on Intelligent Systems and Innovative Computations — The 6th Bellman Continuum, August 1–2, 1994, Hachioji, Tokyo, Japan, to appear in J. Computers and Mathematics.
Leitmann, G.; Lee, C. S.: Stabilization of a Competing Species System, Proceedings of the EUROSIM Congress ′95, September 11–15, Vienna, Austria.
Cromer, T. L.: Seasonal control for an endemic disease with seasonal fluctuations, Theoretical Population Biology, Vol. 33, pp. 115–125, 1988.
Hethcote, H. W.: Asymptotic behavior in a deterministic epidemic model, Bulletin of Mathematical Biology, Vol. 35, pp. 607–614, 1973.
Lajmanovich, A.; Yorke, J. A.: A deterministic model for gonorrhea in a nonhomogeneous population, Mathematical Biosciences, Vol. 28, pp. 221–236, 1976.
Hethcote, H. W.; Yorke, J. A.: Gonorrhea Transmission Dynamics and Control, Springer-Verlag, New York, 1985.
Cooke, K. L.; Kaplan, J. L.: A periodicity threshold theorem for epidemics and population growth, Mathematical Biosciences, Vol. 31, pp. 87–104, 1976.
Smith, H. L.: On periodic solutions of a delay integral equation modeling epidemics, Journal of Mathematical Biology, Vol. 4, pp. 69–80, 1977.
Nussbaum, R. D.: A periodicity threshold theorem for some nonlinear integral equations, SIAM Journal of Mathematical Analysis, Vol. 9, pp. 356–376, 1978.
Cromer, T. L.: Asymptotically periodic solutions to Volterra integral equations in epidemic models, Journal of Mathematical Analysis and Applications, Vol. 110, No. 2, pp. 483–494, 1985.
Yorke, J. A.; Hethcote, H. W.; Nold, A.: Dynamics and control of the transmission of gonorrhea, Sex. Transm. Dis. Vol. 5, No. 2, pp. 51–56, 1978.
Lee, C. S.; Leitmann, G.: Control Strategies for an Endemic Disease in the Presence of Uncertainty, in Recent Trends in Optimization Theory and Applications, edited by R.P. Agarwal, World Scientific, Singapore, 1994.
Leitmann, G.: Guaranteed Ultimate Boundedness for a Class of Uncertain Linear Dynamical Systems, IEEE Transactions on Autom. Control, Vol. AC-23, No. 6, pp. 1109–1110, 1978.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer Basel AG
About this paper
Cite this paper
Leitmann, G. (1998). The Use of Screening for the Control of an Endemic Disease. In: Schmidt, W.H., Heier, K., Bittner, L., Bulirsch, R. (eds) Variational Calculus, Optimal Control and Applications. International Series of Numerical Mathematics, vol 124. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8802-8_29
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8802-8_29
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9780-8
Online ISBN: 978-3-0348-8802-8
eBook Packages: Springer Book Archive