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Approaches to the Control of Infectious Disease

Published online by Cambridge University Press:  05 September 2017

T Norman  and
J Bailey
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Abstract

Maurice Bartlett's work on the mathematical theory of epidemics, recurrent epidemics and endemicity over the years 1953–66 has helped to stimulate a wide range of applied studies of practical importance. This paper reviews contemporary trends in the control of infectious disease. Historically, the subject started in response to very practical problems, but subsequent developments showed an increasingly marked divergence between general theory and practical applications. In recent years, however, improvements in parameter estimation, asymptotic and stochastic approximation, the modelling of individual diseases, advances in computerized simulations, the construction of resource allocation models, the use of control theory, etc., have been gradually leading to a synthesis of the utmost importance to public health action. Models can now be fitted to specific field data; alternative intervention strategies involving immunization, prophylaxis or treatment can be evaluated; and the incorporation of realistic epidemiological models in a wider decision-oriented system dynamics setting may soon help to solve broader strategic problems on the policy level.

Type
Part IX — Biomathematics and Epidemiology
Information
Journal of Applied Probability , Volume 12 , Issue S1 , 1975 , pp. 357 - 372
Copyright
Copyright © 1975 Applied Probability Trust 

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References

Abakuks, A. (1973) An optimal isolation policy for an epidemic. J. Appl. Prob. 10, 247–262.CrossRefGoogle Scholar
Bailey, N. T. J. (1954) A statistical method of estimating the periods of incubation and infection of an infectious disease. Nature 174, 139–140.CrossRefGoogle ScholarPubMed
Bailey, M. T. J. (1967) The simulation of stochastic epidemics in two dimensions. Proc. Fifth Berkeley Symp. Math. Statist. Prob. 4, 237–257.Google Scholar
Bailey, N. T. J. (1975) The Mathematical Theory of Infectious Diseases. Griffin, London. To appear.Google Scholar
Bailey, N. T. J. and Alff-Steinberger, C. (1970) Improvements in the estimation of latent and infectious periods of a contagious disease. Biometrika 57, 141–153.Google Scholar
Bailey, N. T. J. and Thomas, A. S. (1971) The estimation of parameters from population data on the general stochastic epidemic. Theor. Pop. Biol. 2, 253–270. (Summarized in Adv. Appl. Prob. 3. 211–214.) Google Scholar
Bartlett, M. S. (1953) Stochastic processes or the statistics of change. Appl. Statist. 2, 44–64.Google Scholar
Bartlett, M. S. (1956) Deterministic and stochastic models for recurrent epidemics. Proc. Third Berkeley Symp. Math. Statist. Prob. 4, 81–109.Google Scholar
Bartlett, M. S. (1957) Measles periodicity and community size. J. R. Statist. Soc. Ser. A 120, 48–70.Google Scholar
Bartlett, M. S. (1960a) Stochastic Population Models in Ecology and Epidemiology. Methuen and Co. Ltd., London.Google Scholar
Bartlett, M. S. (1960b) Some stochastic models in ecology and epidemiology. In Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling (eds. Olkin, I. et al.), 89–96. Stanford University Press.Google Scholar
Bartlett, M. S. (1960C) The critical community size for measles in the United States. J. R. Statist. Soc. Ser. A. 123, 37–44.Google Scholar
Bartlett, M. S. (1961) Monte Carlo studies in ecology and epidemiology. Proc. Fourth Berkeley Symp. Math. Statist. Prob. 4, 39–55.Google Scholar
Bartlett, M. S. (1964) The relevance of stochastic models for large-scale epidemiological phenomena. Appl. Statist. 13, 2–8.Google Scholar
Bartlett, M. S. (1966) Some notes on epidemiological theory. In Research Papers in Statistics: Festschrift for J. Neyman (ed. David, F. N.), 25–36. Wiley, New York.Google Scholar
Becker, N. G. (1972) Vaccination programs for rare infectious diseases. Biometrika 59, 443–453.Google Scholar
Black, F. L. (1966) Measles endemicity in insular populations: critical community size and its evolutionary implications. J. Theor. Biol. 11, 207–211.Google Scholar
Br⊘Gger, S. (1967) Systems analysis in tuberculosis control: a model. Amer. Rev. Resp. Dis. 95, 421–434.Google Scholar
Cvjetanovic, B. (1972) Use of mathematical models in the planning and evaluation of control measures against infectious diseases. J. Egypt. Pub. Hlth Assoc. 47, 121–128.Google Scholar
Cvjetanovic, B., Grab, B. and Uemura, K. (1971) Epidemiological model of typhoid fever and its use in planning and evaluation of antityphoid immunization and sanitation programmes. Bull. Wld Hlth Org. 45, 53–75.Google Scholar
Cvjetanovic, B., Grab, B., Uemura, K. and Bytchenko, B. (1972) Epidemiological model of tetanus and its use in the planning of immunization programmes. Int. J. Epid. 1, 125–137.CrossRefGoogle ScholarPubMed
Cvjetanovic, B., Uemura, K., Grab, B. and Sundaresan, T. (1973) Use of mathematical models in the evaluation of the effectiveness of preventive measures against some infectious diseases. Proc. Sixth Int. Sci. Meeting, Int. Epid. Assoc. 2, 913–933.Google Scholar
Dietz, K., Molineaux, L. and Thomas, A. (1974) A malaria model tested in the African Savannah. Bull. Wld Hlth Org. 50, 347–357.Google ScholarPubMed
Feldstein, M. S., Piot, M. A. and Sundaresan, T.K. (1973) Resource allocation model for public health planning. Bull. Wld Hlth Org. 48, Supp., 3–108.Google ScholarPubMed
Goffman, W. and Warren, K. S. (1970) An application of the Kermack-McKendrick theory to the epidemiology of schistosomiasis. Amer. J. Trop. Med. Hyg. 19, 278–283.Google Scholar
Greenwood, M. (1931) On the statistical measure of infectiousness. J. Hyg. Camb. 31, 336–351.Google Scholar
Gupta, N.K. and Rink, R. E. (1971) A model for communicable disease control. Proc. 24th Ann. Conf. Eng. Med. Biol. Las Vegas.Google Scholar
Gupta, N. K. and Rink, R. E. (1973) Optimal control of epidemics. Math. Biosci. 18, 383–396.Google Scholar
Hairston, N. G. (1962) Population ecology and epidemiological problems. In CIBA Foundation Symposium on Bilharziasis (ed. Wolstenholme, C. E. W. and O'Connor, M.), 36–62. Churchill, London.Google Scholar
Hairston, N. G. (1965a) On the mathematical analysis of schistosome populations. Bull. Wld Hlth Org. 33, 45–62.Google Scholar
Hairston, N. G. (1965b) An analysis of age-prevalence data by catalytic models. A contribution to the study of bilharziasis. Bull. Wld Hlth Org. 33, 163–175.Google Scholar
Hamer, W. H. (1906) Epidemic disease in England. Lancet 1, 733–739.Google Scholar
Hethcote, H. W. (1970) Note on determining the limiting susceptible population in an epidemic model. Math. Biosci. 9, 161–163.Google Scholar
Hethcote, H. W. and Waltman, P. (1973) Optimal vaccination schedules in a deterministic epidemic model. Math. Biosci. 18, 365–381.Google Scholar
Jaquette, D. L. (1970) A stochastic model for the optimal control of epidemics and pest populations. Math. Biosci. 8, 343–354.Google Scholar
Kendall, D.G. (1956) Deterministic and stochastic epidemics in closed populations. Proc. Third Berkeley Symp. Math. Statist. Prob. 4, 149–165.Google Scholar
Kendall, D. G. (1965) Mathematical models of the spread of infection. In Mathematics and Computer Science in Biology and Medicine. H.M.S.O., London, 213–225.Google Scholar
Kermack, W. O. and Mckendrick, A. G. (1927–39) Contributions to the mathematical theory of epidemics. Proc. Roy. Soc. A 115, 700–721. (Part I, 1927.) Proc. Roy. Soc. A 138, 55–83. (Part II, 1932.) Proc. Roy. Soc. A 141, 94–122.(Part III, 1933.) J. Hyg. Camb. 37, 172–187. (Part IV, 1937.) J. Hyg. Camb. 39, 271–288. (Part V, 1939.) Google Scholar
Leyton, M.K. (1968) Stochastic models in populations of helminthic parasites in the definitive host, II: sexual mating functions. Math. Biosci. 3, 413–419.Google Scholar
Linhart, H. (1968) On some bilharzia infection and immunization models. S. Afr. Statist. J. 2, 61–66.Google Scholar
Lotka, A. J. (1923) Contributions to the analysis of malaria epidemiology. Amer. J. Hyg. 3, (Suppl. 1), 1–121.Google Scholar
Ludwig, D. (1973) Stochastic approximation for the general epidemic. J. Appl. Prob. 10, 263–276.Google Scholar
Lynn, W. R. and Revelle, C. S. (1968) Workshop on model methodology for health planning, with particular reference to tuberculosis. Amer. Rev. Resp. Dis. 98, 687–691.Google Scholar
Macdonald, G. (1950a) The analysis of infection rates in diseases in which superinfection occurs. Trop. Dis. Bull. 47, 907–915.Google Scholar
Macdonald, G. (1950b) The analysis of malaria parasite rates in infants. Trop. Dis. Bull. 47, 915–938.Google Scholar
Macdonald, G. (1952a) The analysis of the sporozoite rate. Trop. Dis. Bull. 49, 569–586.Google Scholar
Macdonald, G. (1952b) The analysis of equilibrium in malaria. Trop. Dis. Bull. 49, 813–829.Google Scholar
Macdonald, G. (1953) The analysis of malaria epidemics. Trop. Dis. Bull. 50, 871–889.Google ScholarPubMed
Macdonald, G. (1955) The measurement of malaria transmission. Proc. Roy. Soc. Med. 48, 295–301.Google Scholar
Macdonald, G. (1957) The Epidemiology and Control of Malaria. Oxford University Press, London.Google Scholar
Macdonald, G. (1965a) The dynamics of helminth infections, with special reference to schistosomes. Trans. Roy. Soc. Trop. Med. Hyg. 59, 489–506.CrossRefGoogle ScholarPubMed
Macdonald, G. (1965b) On the scientific basis of tropical hygiene. Trans. Roy. Soc. Trop. Med. Hyg. 59, 611–620.Google Scholar
Macdonald, G. (1965c) Eradication of malaria. Pub. Hlth Rep. 80, 870–880.Google Scholar
Macdonald, G. (1973) Dynamics of Tropical Diseases. Oxford University Press, London.Google Scholar
Macdonald, G., Cuellar, C. B. and Foll, C. V. (1968) The dynamics of malaria. Bull. Wld Hlth Org. 38, 743–755.Google Scholar
Macdonald, G. and Göckel, C. W. (1964) The malaria parasite rate and interruption of transmission. Bull. Wld Hlth Org. 31, 365–377.Google Scholar
Mahler, H. T. and Piot, M. A. (1966a) Essais d'application de la recherche opérationnelle dans la lutte antituberculose. I: formulation des problèmes, rassemblement des données, choix de modèles. Bull. INSERM 21, 855–881.Google Scholar
Mahler, H. T. and Piot, M. A. (1966b) Essais d'application de la recherche opérationnelle dans la lutte antituberculose. II: programmation linéaire: problèmes conceptuels et d'application. Bull. INSERM 21, 1021–1045.Google Scholar
Mollison, D. (1970) Spatial propagation of simple epidemics. Ph. D. Thesis, Statistical Laboratory, Cambridge University.Google Scholar
Mollison, D. (1972a) Possible velocities for a simple epidemic. Adv. Appl. Prob. 4, 233–257.Google Scholar
Mollison, D. (1972b) The rate of spatial propagation of simple epidemics. Proc. Sixth Berkeley Symp. Math. Statist. Prob. 3, 579–614.Google Scholar
Morton, R. and Wickwire, K. H. (1974) On the optimal control of a deterministic epidemic. Adv. Appl. Prob. 6, 622–635.Google Scholar
Nåsell, I. (1972) Mathematical models of some parasitic diseases involving an intermediate host. Ph. D. Thesis, New York University.Google Scholar
Nåsell, I. and Hirsch, W. M. (1971) Mathematical models of some parasitic diseases involving an intermediate host. Report No. IMM393. Courant Institute of Mathematical Sciences, New York.Google Scholar
Nåsell, I. and Hirsch, W. M. (1972) A mathematical model of some helminthic infections. Comm. Pure Appl. Math. 25, 459–477.Google Scholar
Nåsell, I. and Hirsch, W. M. (1973a) The transmission dynamics of schistosomiasis. Comm. Pure Appl. Appl. Math. 26, 395–453.Google Scholar
Nåsell, I. and Hirsch, W. M. (1973b) The transmision and control of schistosome infections. Working Proceedings of NATO Conference on ‘Mathematical Analysis of Decision Problems in Ecology’, Istanbul, 9–13 July 1973.Google Scholar
Revelle, C. (1967) The economic allocation of tuberculosis control activities in developing nations. Ph. D. Thesis, Cornell University.Google Scholar
Revelle, C., Feldmann, F. and Lynn, W. (1969) An optimization model of tuberculosis epidemiology. Management Sci. 16, B190–B211.Google Scholar
Revelle, C. Lynn, W. R. and Feldmann, F. (1967) Mathematical models for the economic allocation of tuberculosis control activities in developing countries. Amer. Rev. Resp. Dis. 96, 893–909.Google Scholar
Revelle, C. and Male, J. (1970) A mathematical model for determining case finding and treatment activities in tuberculosis control programs. Amer. Rev. Resp. Dis. 102, 403–411.Google Scholar
Ross, R. (1911) The Prevention of Malaria (2nd edn.) Murray, London.Google Scholar
Sanders, J. L. (1971) Quantitative guidelines for communicable disease control programs. Biometrics 27, 883–893.Google Scholar
Soper, H. E. (1929) Interpretation of perodicity in disease-prevalence. J. R. Statist. Soc. 92, 34–73.Google Scholar
Tallis, G. M. and Leyton, M. K. (1966) A stochastic approach to the study of parasite populations. J. Theor. Biol. 13, 251–260.Google Scholar
Taylor, H. M. (1968) Some models in epidemic control. Math. Biosci. 3, 383–398.Google Scholar
Waaler, H. T., Geser, A. and Andersen, S. (1962) The use of mathematical models in the study of the epidemiology of tuberculosis. Amer. J. Publ. Hlth 52, 1002–1013.CrossRefGoogle Scholar
Whittle, P. (1955) The outcome of a stochastic epidemic—a note on Bailey's paper. Biometrika 42, 116–122.Google Scholar