Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-10T16:31:59.809Z Has data issue: false hasContentIssue false
  • English
  • Français

Mathematical modelling and theory for estimating the basic reproduction number of canine leishmaniasis

Published online by Cambridge University Press:  06 April 2009

G. Hasibeder ,
C. Dye  and
J. Carpenter
G. Hasibeder
Affiliation:
Abteilung für Mathematische Biologie, Technische Universität Wien, Wiedner Hauptstrasse 8/118, A-1040 Wien, Austria
C. Dye
Affiliation:
Department of Medical Parasitology, London School of Hygiene and Tropical Medicine, Keppel Street, London WC 1E 7HT, UK
J. Carpenter
Affiliation:
Department of Mathematics, University of Warwick, Coventry CV4 7AL, UK
Get access Rights & Permissions [Opens in a new window]

Extract

The paper describes a mathematical model for canine leishmaniasis and presents formulae which can be used to estimate the basic reproduction number, R0. The primary concern has been to devise methods of estimation which make best use of those data most easily obtained by fieldwork, e.g. surveys of prevalence in dog (by age) and sandfly populations. A range of formulae are offered which are more or less demanding of data, and which consequently give more or less precise estimates of R0. They include methods for assessing the influence on R0 of heterogeneous biting rates of sandflies on dogs, in which the essence of heterogeneous transmission can be captured merely by measuring relative rather than absolute contact rates.

Keywords

canine leishmaniasisepidemiologyheterogeneous transmissionmathematical modelbasic reproduction numberforce of infectionsandflies.
Type
Research Article
Information
Parasitology , Volume 105 , Issue 1 , August 1992 , pp. 43 - 53
Copyright
Copyright © Cambridge University Press 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Adler, S. & Theodor, O. (1932). Investigations on Mediterranean Kala-azar. VI. Canine visceral leishmaniasis. Proceedings of the Royal Society, B 110, 402–12.Google Scholar
Anderson, R. M. & May, R. M. (1991). Infectious Diseases of Humans: Dynamics and Control. Oxford: Oxford University Press.CrossRefGoogle Scholar
Diekmann, O., Heesterbeek, J. A. P. & Metz, J. A. J. (1990). On the definition and the computation of the basic reproduction ratio R 0 in models for infectious diseases in heterogeneous populations. Journal of Mathematical Biology 28, 365–82.CrossRefGoogle ScholarPubMed
Dye, C. (1992). The analysis of parasite transmission by bloodsucking insects. Annual Review of Entomology 37, 1–19.CrossRefGoogle ScholarPubMed
Dye, C. & Hasibeder, G. (1986). Population dynamics of mosquito-borne disease: effects of flies which bite some people more frequently than others. Transactions of the Royal Society of Tropical Medicine and Hygiene 80, 69–77.CrossRefGoogle ScholarPubMed
Dye, C., Killick-Kendrick, R., Vitutia, M. M., Walton, R., Killick-Kendrick, M., Harith, A. E., Guy, M. W., Cañavate, M.-C. & Hasibeder, G. (1992). Epidemiology of canine leishmaniasis: prevalence, incidence and basic reproduction number calculated from a cross-sectional serological survey on the island of Gozo, Malta. Parasitology 105, 35–41.CrossRefGoogle ScholarPubMed
Gradoni, L., Maroli, M., Gramiccia, M. & Mancianti, F. (1987). Leishmania infantum infection rates in Phlebotomus perniciosus fed on naturally infected dogs under antimonial treatment. Medical and Veterinary Entomology 1, 339–42.CrossRefGoogle ScholarPubMed
Hasibeder, G. & Dye, C. (1988). Population dynamics of mosquito-borne disease: persistence in a completely heterogeneous environment. Theoretical Population Biology 33, 31–53.CrossRefGoogle Scholar
Jacquez, J. A, Simon, C. P. & Koopman, J. S. (1991). The reproduction number in deterministic models of contagious diseases. Comments on Theoretical Biology 2, 159–209.Google Scholar
Lainson, R., Dye, C., Shaw, J. J., Macdonald, D., Courtenay, O., Souza, A. A. A. & Silveira, F. T. (1990). Amazonian visceral leishmaniasis: distribution of the vector Lutzomyia longipalpis (Lutz & Neiva) in relation to the fox Cerdocyon thous (L.) and the efficiency of this reservoir host as a source of infection. Memorias do Instituto Oswaldo Cruz 85, 135–7.CrossRefGoogle Scholar
Lanotte, G., Rioux, J.-A., Perieres, J. & Vollhardt, Y. (1979). Ecologie des leishmanioses dans le sud de la France. 10. Les formes évolutives de la leishmaniose viscérale canine. Elaboration d'une typologie bioclinique à finalité épidémiologique. Annales de Parasitologie 54, 277–95.Google Scholar
Nokes, D. J. & Anderson, R. M. (1988). The use of mathematical models in the epidemiological study of infectious diseases and in the design of mass immunization programmes. Epidemiology and Infection 101, 1–20.CrossRefGoogle ScholarPubMed
Rioux, J.-A., Lanotte, G., Croset, H. & Dedet, J. P. (1972). Ecologie des leishmanioses dans le sud de la France. 5. Pouvoir infestant comparé des diverses formes de leishmaniose canine vis-à-vis de Phlebotomus ariasi Tonnoir, 1921. Annales de Parasitologie Humaine et Comparée 47, 413–19.CrossRefGoogle Scholar