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The periodicity of endemic malaria

Published online by Cambridge University Press:  14 July 2016

J. Radcliffe
J. Radcliffe*
Affiliation:
Queen Mary College, London
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Abstract

In many endemic areas the level of infection of malaria exhibits a regular cycle. A stochastic model is formulated to describe endemic malaria and is used to justify a set of deterministic equations. The model incorporates the properties peculiar to malaria, i.e., in endemic areas malaria is not usually fatal and an individual can be and usually is reinfected. The theory of small oscillations is applied to the deterministic equations, and under the assumption of stable populations of hosts and vectors an expression is obtained for the period of oscillation of the infection.

Keywords

ENDEMIC MALARIAHOST-VECTOR RECURRENT EPIDEMICPERIOD OF OSCILLATION
Type
Short Communications
Information
Journal of Applied Probability , Volume 11 , Issue 3 , September 1974 , pp. 562 - 567
Copyright
Copyright © Applied Probability Trust 1974 

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References

Bailey, N. T. J. (1957) The Mathematical Theory of Epidemics. Griffin, London.Google Scholar
Bartlett, M. S. (1956) Deterministic and stochastic models for recurrent epidemics. Proc. 3rd Berkeley Symp. Math. Statist. Prob. 4, 81–109.Google Scholar
Bartlett, M. S. (1960) Stochastic Population Models in Ecology and Epidemiology. Wiley, New York; Methuen, London.Google Scholar
Bartlett, M. S. (1964) The relevance of stochastic models for large-scale epidemiological phenomena. Applied Statistics 13, 2–8.CrossRefGoogle Scholar
Bartlett, M. S. (1966) Some notes on epidemiological theory. Research Papers in Statistics, Festschrift for J. Neyman. (Ed. David, F. N.) Wiley, New York.Google Scholar
Bruce-Chwatt, L. J. (1969) Quantitative epidemiology of tropical diseases. Transactions of the Royal Society of Tropical Medicine and Hygiene 63, 131–143. Reprinted in Dynamics of Tropical Disease. (Ed. Bruce-Chwatt, J. L. and Glanville, V. J.) (1973) Oxford University Press, London.CrossRefGoogle ScholarPubMed
Gillett, J. D. (1971) Mosquitos. Weidenfeld and Nicolson, London.Google Scholar
Macdonald, G. (1931) The mechanism of infection with malaria in children living under endemic and hyperendemic conditions. Indian Journal of Medical Research 18, 1347–1372. Reprinted in Dynamics of Tropical Disease. (Ed. Bruce-Chwatt, L. J. and Glanville, V. J.) (1973) Oxford University Press, London.Google Scholar
Macdonald, G. (1950) The analysis of malaria parasite rates in infants. Tropical Diseases Bulletin 47, 915–938. Reprinted in Dynamics of Tropical Disease. (Ed. Bruce-Chwatt, L. J. and Glanville, V. J.) (1973) Oxford University Press, London.Google ScholarPubMed
Macdonald, G. (1953) The analysis of malaria epidemics. Tropical Diseases Bulletin 50, 871–889. Reprinted in Dynamics of Tropical Disease. (Ed. Bruce-Chwatt, L. J. and Glanville, V. J.) (1973) Oxford University Press, London.Google ScholarPubMed
Radcliffe, J. (1973) The initial geographical spread of host-vector carrier-borne epidemics. J. Appl. Prob. 10, 703–717.CrossRefGoogle Scholar