Skip to main content
×
Home
    • Aa
    • Aa

A general model for the African trypanosomiases

  • D. J. Rogers (a1)
Abstract
SUMMARY

A general mathematical model of a vector-borne disease involving two vertebrate host species and one insect vector species is described. The model is easily extended to other situations involving more than two hosts and one vector species. The model, which was developed from the single-host model for malaria described by Aron & May (1982), is applied to the African trypanosomiases and allows for incubation and immune periods in the two host species and for variable efficiency of transmission of different trypanosome species from the vertebrates to the vectors and vice versa. Equations are derived for equilibrium disease prevalence in each of the species involved. Model predictions are examined by 3-dimensional phase-plane analysis, which is presented as a simple extension of the 2-dimensional phase-plane analysis of the malaria model. Parameter values appropriate for the African trypanosomiases are derived from the literature, and a typical West African village situation is considered, with 300 humans, 50 domestic animals and an average population of 5000 tsetse flies. The model predicts equilibrium prevalences of Trypanosoma vivax, T. congolense and T. brucei of 47·0, 45·8 and 28·7% respectively in the animal hosts, 24·2, 3·4 and 0·15% in the tsetse vectors, and a 7·0% infection of humans with human-infective T. brucei. The contribution to the basic rate of reproduction of the human-infective T. brucei is only 0·11 from the human hosts and 2·54 from the animal hosts, indicating that in the situation modelled human sleeping sickness cannot be maintained in the human hosts alone. The animal reservoir is therefore crucial in determining not only the continued occurrence of the disease in humans, but its prevalence in these hosts as well. The effect of changing average fly density on equilibrium disease prevalences is examined, together with the effect of seasonal changes in fly numbers on disease incidence. In a seasonal situation changes in fly mortality rates affect both future population size and infection rate. Peak disease incidence lags behind peak fly numbers, and that in the less favoured host lags behind that in the more favoured host. Near the threshold fly density for disease transmission disease incidence is more changeable than at higher fly densities and may even exceed equilibrium prevalence at the same average fly density (because most hosts are susceptible at the time that fly numbers begin their annual increase). The implications of the model for disease control are discussed. Identifying the precise role of the animal reservoir may suggest that treating such animals will achieve a greater reduction of human sleeping sickness than direct treatment of the humans alone. Statistically significant results of control campaigns may also be more easily shown by monitoring the non-human reservoirs. The model provides a means by which a correct perspective view can be obtained of the complex epidemiology and epizootiology of the African trypanosomiases.

Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

R. M. Anderson (1982). Population Dynamics of Infectious Diseases. London: Chapman and Hall.

J. L. Aron & R. M. May (1982). The population dynamics of malaria. In Population Dynamics of Infectious Diseases (ed. R. M. Anderson ), pp. 139–79. London: Chapman and Hall.

M. T. Ashcroft , E. Burtt & H. Fairbairn (1959). The experimental infection of some African wild animals with Trypanosoma rhodesiense, T. brucei and T. congolense. Annals of Tropical Medicine and Parasitology 53, 147–61.

D. Bruce , A. E. Hamerton , H. R. Bateman & F. P. Mackie (1910). Mechanical transmission of Sleeping Sickness by the tsetse fly. Proceedings of the Royal Society of London, B 82, 498501.

J. B. Gingrich , R. A. Ward , L. M. Macken & M. J. Schoenbechler (1982 a). Trypanosoma brucei rhodesiense (Trypanosomatidae): factors influencing infection rates of a recent human isolate in the tsetse Glossina morsitans (Diptera, Glossinidae). Journal of Medical Entomology 19, 268–74.

J. B. Gingrich , R. A. Ward , L. M. Macken & K. M. Esser (1982 b). African sleeping sickness: new evidence that mature tsetse flies (Glossina morsitans) can become potent vectors. Transactions of the Royal Society of Tropical Medicine and Hygiene 76, 479–81.

J. B. Gingrich , L. W. Roberts & L. M. Macken (1983). Trypanosoma brucei rhodesiense: mechanical transmission by tsetse, Glossina morsitans (Diptera, Glossinidae), in the laboratory. Journal of Medical Entomology 20, 673–6.

T. Habtemariam , R. Ruppanner , H. P. Riemann & J. H. Theis (1983 a). An epidemiologic systems analysis model for African trypanosomiasis. Preventive Veterinary Medicine 1, 125–36.

T. Habtemariam , R. Ruppanner , H. P. Riemann & J. H. Theis (1983 b). Epidemic and endemic characteristics of trypanosomiasis in cattle: a simulation model. Preventive Veterinary Medicine 1, 137–45.

L. Jenni , D. H. Molyneux , J. L. Livesey & R. Galun (1980). Feeding behaviour of tsetse flies infected with salivarian trypanosomes. Nature, London 283, 383–5.

J. Maynard Smith & M. Slatkin (1973). The stability of predator-prey systems. Ecology 54, 384–91.

S. K. Moloo & F. Dar (1985). Probing by Glossina morsitans centralis infected with pathogenic Trypanosoma species. Transactions of the Royal Society of Tropical Medicine and Hygiene 79, 119.

M. Murray & A. R. Gray (1984). The current situation on animal trypanosomiasis in Africa. Preventive Veterinary Medicine 2, 2330.

M. Murray , W. I. Morrison & D. D. Whitelaw (1982). Host susceptibility to African trypanosomiasis: trypanotolerance. Advances in Parasitology 21, 168.

L. H. Otieno & N. Darji (1979). The abundance of pathogenic African trypanosomes in the salivary secretions of wild Glossina pallidipes. Annals of Tropical Medicine and Parasitology 73, 583–8.

D. Rogers (1977). Study of a natural population of Glossina fuscipes fuscipes Newstead and a model of fly movement. Journal of Animal Ecology 46, 309–30.

R. Ross (1916). An application of the theory of probabilities to the study of a priori pathometry. I. Proceedings of the Royal Society of London, A 92, 204–30.

E. A. Wells (1972). The importance of mechanical transmission in the epidemiology of nagana: a review. Tropical Animal Health and Production 4, 7488.

A. J. Wilson , F. K. Dar & J. Paris (1972). A study on the transmission of salivarian trypanosomes isolated from wild tsetse flies. Tropical Animal Health and Production 4, 1422.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Parasitology
  • ISSN: 0031-1820
  • EISSN: 1469-8161
  • URL: /core/journals/parasitology
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 28 *
Loading metrics...

Abstract views

Total abstract views: 175 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 25th June 2017. This data will be updated every 24 hours.