Optimum control of epidemics. (English) Zbl 0267.92006


92D25 Population dynamics (general)
93C15 Control/observation systems governed by ordinary differential equations
93B99 Controllability, observability, and system structure
Full Text: DOI


[1] Bailey, N. T.J., The Mathematical Theory of Epidemics (1957), Griffin: Griffin London · Zbl 0115.37202
[2] ReVelle, C. S., Mathematical models for the economic allocation of tuberculosis control activities in developing nations, Amer. Rev. Resp. Dis., 96, 893-909 (1967)
[3] Jaquette, D. L., A stochastic model for the optimum control of epidemics and pest populations, Mathematical Biosciences, 8, 343-354 (1970) · Zbl 0201.22702
[4] Taylor, Howard M., Some models in epidemic control, Mathematical Biosciences, 3, 383-398 (1968)
[5] Gupta, N. K.; Rink, R. E., A model for communicable disease control, Proceedings 24th Annual Conference on Engineering in Medicine and Biology, 13, 296 (1971), Las Vegas
[6] Simpson, R. E.Hope, Infectiousness of communicable diseases in the household, Lancet, 263, 549-554 (1952)
[7] Bailey, N. T.J.; Steinberger, C. A., Improvements in estimation of latent and infectious periods of contagious diseases, Biometrika, 57, 141-153 (1970)
[8] Gupta, N. K., Modeling and Optimum Control of Epidemics, Ph.D. Thesis (1972), University of Alberta
[9] Hoppensteadt, F.; Waltman, P., A problem in the theory of epidemics, Mathematical Biosciences, 9, 71-91 (1970) · Zbl 0212.52105
[10] McAulay, R. J., A gradient method for systems with the time delays and its application to waveform design, IEEE Trans. Automatic Control, AC14, 230-237 (1969)
[11] Budelis, J. J.; Bryson, A. E., Some optimal control results for differential difference systems, IEEE Trans. Automatic Control, AC15, 237-241 (1970)
[12] Pontryagin, L. S., The Mathematical Theory of Optimum Processes (1962), Wiley: Wiley New York · Zbl 0112.05502
[13] Kharatishvili, G. L., A maximum principle in extremal problems with delays, (Balakrishnan, A. V.; Neustadt, L. W., Mathematical Theory of Control (1967), Academic: Academic New York), 26-34 · Zbl 0216.17701
[14] Lasdon, L. S.; Mitter, S. K.; Waren, A. D., The conjugate gradient method for optimum control problems, IEEE Trans. Automatic Control, AC12, 132-138 (1967)
[15] Gottlieb, R. G., Rapid Convergence to optimum solution using a Min-H strategy, AIAA, 5, 322-329 (1967) · Zbl 0183.16702
[16] Pierre, D. A., Optimization Theory with Applications, Chapter 6: Search Techniques and Non-linear Programming (1969), Wiley: Wiley New York · Zbl 0205.15503
[17] Kelley, H. J., Methods of gradients, (Leitmann, George, Optimization Techniques (1962), Academic: Academic New York) · Zbl 0167.08803
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