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The Use of Screening for the Control of an Endemic Disease

  • Georg Leitmann
Part of the International Series of Numerical Mathematics book series (ISNM, volume 124)

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.

Keywords

Infected Individual Epidemic Model Public Health Authority Infected Population Endemic Disease 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Corless, M.; Leitmann, G.: Bounded controllers for robust exponential convergence, Journal of Optimization Theory and Applications, Vol. 76, pp. 1–12, 1993.MathSciNetzbMATHCrossRefGoogle Scholar
  2. [2]
    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.Google Scholar
  3. [3]
    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.Google Scholar
  4. [4]
    Leitmann, G.; Lee, C. S.: Stabilization of a Competing Species System, Proceedings of the EUROSIM Congress ′95, September 11–15, Vienna, Austria.Google Scholar
  5. [5]
    Cromer, T. L.: Seasonal control for an endemic disease with seasonal fluctuations, Theoretical Population Biology, Vol. 33, pp. 115–125, 1988.MathSciNetzbMATHCrossRefGoogle Scholar
  6. [6]
    Hethcote, H. W.: Asymptotic behavior in a deterministic epidemic model, Bulletin of Mathematical Biology, Vol. 35, pp. 607–614, 1973.zbMATHGoogle Scholar
  7. [7]
    Lajmanovich, A.; Yorke, J. A.: A deterministic model for gonorrhea in a nonhomogeneous population, Mathematical Biosciences, Vol. 28, pp. 221–236, 1976.MathSciNetzbMATHCrossRefGoogle Scholar
  8. [8]
    Hethcote, H. W.; Yorke, J. A.: Gonorrhea Transmission Dynamics and Control, Springer-Verlag, New York, 1985.Google Scholar
  9. [9]
    Cooke, K. L.; Kaplan, J. L.: A periodicity threshold theorem for epidemics and population growth, Mathematical Biosciences, Vol. 31, pp. 87–104, 1976.MathSciNetzbMATHCrossRefGoogle Scholar
  10. [10]
    Smith, H. L.: On periodic solutions of a delay integral equation modeling epidemics, Journal of Mathematical Biology, Vol. 4, pp. 69–80, 1977.MathSciNetzbMATHCrossRefGoogle Scholar
  11. [11]
    Nussbaum, R. D.: A periodicity threshold theorem for some nonlinear integral equations, SIAM Journal of Mathematical Analysis, Vol. 9, pp. 356–376, 1978.MathSciNetzbMATHCrossRefGoogle Scholar
  12. [12]
    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.MathSciNetzbMATHCrossRefGoogle Scholar
  13. [13]
    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.CrossRefGoogle Scholar
  14. [14]
    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.Google Scholar
  15. [15]
    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.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Basel AG 1998

Authors and Affiliations

  • Georg Leitmann
    • 1
  1. 1.College of EngineeringUniversity of CaliforniaBerkeleyUSA

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