{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T01:04:27Z","timestamp":1791162267043,"version":"4.1.0"},"reference-count":54,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2009,4,6]],"date-time":"2009-04-06T00:00:00Z","timestamp":1238976000000},"content-version":"unspecified","delay-in-days":7553,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Parasitology"],"published-print":{"date-parts":[[1988,8]]},"abstract":"<jats:title>SUMMARY<\/jats:title><jats:p>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 &amp; 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 <jats:italic>vice versa<\/jats:italic>. 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 <jats:italic>Trypanosoma vivax, T. congolense<\/jats:italic> and <jats:italic>T. brucei<\/jats:italic> of 47\u00b70, 45\u00b78 and 28\u00b77% respectively in the animal hosts, 24\u00b72, 3\u00b74 and 0\u00b715% in the tsetse vectors, and a 7\u00b70% infection of humans with human-infective <jats:italic>T. brucei<\/jats:italic>. The contribution to the basic rate of reproduction of the human-infective <jats:italic>T. brucei<\/jats:italic> is only 0\u00b711 from the human hosts and 2\u00b754 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.<\/jats:p>","DOI":"10.1017\/s0031182000066853","type":"journal-article","created":{"date-parts":[[2009,6,5]],"date-time":"2009-06-05T16:10:34Z","timestamp":1244218234000},"page":"193-212","source":"Crossref","is-referenced-by-count":128,"title":["A general model for the African trypanosomiases"],"prefix":"10.1017","volume":"97","author":[{"given":"D. J.","family":"Rogers","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2009,4,6]]},"reference":[{"key":"S0031182000066853_ref054","first-page":"319","volume-title":"International Scientific Committee for Trypanosomiasis Research, Seventh Meeting, Bruxelles, 1958","author":"Wijers","year":"1960"},{"key":"S0031182000066853_ref053","unstructured":"W.H.O. (1986). Epidemiology and control of African trypanosomiasis. Report of a W.H.O. Expert Committee. W.H.O. Technical Report Series, no. 739. Geneva: World Health Organization."},{"key":"S0031182000066853_ref052","doi-asserted-by":"publisher","DOI":"10.1007\/BF02357090"},{"key":"S0031182000066853_ref051","first-page":"747","article-title":"An observation on the unexpected frequency of some multiple infections","volume":"47","author":"Willett","year":"1972","journal-title":"Bulletin of the World Health Organization"},{"key":"S0031182000066853_ref047","first-page":"216","volume-title":"Tenth International Congress on Tropical Medicine and Malaria","author":"Sachs","year":"1980"},{"key":"S0031182000066853_ref046","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1916.0007"},{"key":"S0031182000066853_ref044","doi-asserted-by":"publisher","DOI":"10.1017\/S0007485300015674"},{"key":"S0031182000066853_ref043","first-page":"24","article-title":"Sleeping sickness survey in the Serengeti area (Tanzania) 1971. II. The vector role of Glossina swynnertoni Austen","volume":"30","author":"Rogers","year":"1973","journal-title":"Acta Tropica"},{"key":"S0031182000066853_ref042","first-page":"5","article-title":"Trypanosomiasis \u2018risk\u2019 or \u2018challenge\u2019: a review","volume":"42","author":"Rogers","year":"1985","journal-title":"Acta Tropica"},{"key":"S0031182000066853_ref041","unstructured":"Rogers D. J. (1980). Epizootiology: the tsetse-cattle interface. Report of the Expert Consultation on Research on Trypanosomiases, 1\u20135 October 1979, Appendix VI, pp. 61\u20137. Rome: FAO (AGA\u2013801)."},{"key":"S0031182000066853_ref040","doi-asserted-by":"publisher","DOI":"10.2307\/3962"},{"key":"S0031182000066853_ref037","doi-asserted-by":"publisher","DOI":"10.1080\/00034983.1979.11687300"},{"key":"S0031182000066853_ref035","first-page":"40","volume-title":"Wildlife Disease Research and Economic Development","author":"Murray","year":"1981"},{"key":"S0031182000066853_ref034","doi-asserted-by":"publisher","DOI":"10.1016\/0167-5877(84)90045-X"},{"key":"S0031182000066853_ref033","doi-asserted-by":"publisher","DOI":"10.1017\/S0007485300022161"},{"key":"S0031182000066853_ref032","doi-asserted-by":"publisher","DOI":"10.1016\/0035-9203(85)90253-6"},{"key":"S0031182000066853_ref030","doi-asserted-by":"publisher","DOI":"10.1017\/S0031182000081774"},{"key":"S0031182000066853_ref029","unstructured":"Mehlitz D. (1986). Le r\u00e9servoir animal de la maladie du sommeil a Trypanosoma brucei gambiense. Etudes et Syntheses de l'I.E.M.V.T. 18. Maisons-Alfort: Institut d'Elevage et de Medecine Veterinaire des Pays Tropicaux."},{"key":"S0031182000066853_ref027","doi-asserted-by":"publisher","DOI":"10.2307\/1934346"},{"key":"S0031182000066853_ref024","first-page":"813","article-title":"The analysis of equilibrium in malaria","volume":"49","author":"Macdonald","year":"1952","journal-title":"Tropical Diseases Bulletin"},{"key":"S0031182000066853_ref023","doi-asserted-by":"publisher","DOI":"10.1038\/283383a0"},{"key":"S0031182000066853_ref007","doi-asserted-by":"publisher","DOI":"10.1098\/rspb.1910.0044"},{"key":"S0031182000066853_ref009","first-page":"41","volume-title":"The African Trypanosomiases","author":"Duggan","year":"1970"},{"key":"S0031182000066853_ref038","doi-asserted-by":"publisher","DOI":"10.1017\/S0007485300014061"},{"key":"S0031182000066853_ref048","volume-title":"Insect Population Ecology","author":"Varley","year":"1973"},{"key":"S0031182000066853_ref028","first-page":"25","volume-title":"Perspectives in Trypanosomiasis Research","author":"Mehlitz","year":"1982"},{"key":"S0031182000066853_ref049","first-page":"327","volume-title":"International Scientific Committee for Trypanosomiasis Research, Ninth Meeting, Conakry, 1962","author":"Watson","year":"1963"},{"key":"S0031182000066853_ref026","volume-title":"Dynamics of Tropical Disease","author":"Macdonald","year":"1973"},{"key":"S0031182000066853_ref013","doi-asserted-by":"publisher","DOI":"10.1016\/0035-9203(82)90142-0"},{"key":"S0031182000066853_ref008","first-page":"18","volume-title":"Annual Report 1956\u201357. East African Trypanosomiasis Research Organization","author":"Cawdery","year":"1958"},{"key":"S0031182000066853_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-2901-3_5"},{"key":"S0031182000066853_ref036","doi-asserted-by":"publisher","DOI":"10.1016\/S0065-308X(08)60274-2"},{"key":"S0031182000066853_ref022","doi-asserted-by":"publisher","DOI":"10.1017\/S0007485300035434"},{"key":"S0031182000066853_ref018","doi-asserted-by":"publisher","DOI":"10.1016\/0167-5877(83)90017-X"},{"key":"S0031182000066853_ref050","doi-asserted-by":"publisher","DOI":"10.1007\/BF02359739"},{"key":"S0031182000066853_ref039","doi-asserted-by":"publisher","DOI":"10.4269\/ajtmh.1981.30.948"},{"key":"S0031182000066853_ref006","first-page":"85","article-title":"Local distribution and ecology of Glossina palpalis and G. tachinoides in forest foci of West African human trypanosomiasis, with special reference to associations between peri-domestic tsetse and their hosts","volume":"1","author":"Baldry","year":"1980","journal-title":"Insect Science and its Application"},{"key":"S0031182000066853_ref045","volume-title":"The Prevention of Malaria","author":"Ross","year":"1911"},{"key":"S0031182000066853_ref025","volume-title":"The Epidemiology and Control of Malaria","author":"Macdonald","year":"1957"},{"key":"S0031182000066853_ref020","doi-asserted-by":"publisher","DOI":"10.1016\/0167-5877(83)90019-3"},{"key":"S0031182000066853_ref011","first-page":"211","article-title":"Sleeping sickness survey in Musoma district, Tanzania. IV. Examination of wild animals as potential reservoir of T. rhodesiense","volume":"28","author":"Geigy","year":"1971","journal-title":"Acta Tropica"},{"key":"S0031182000066853_ref031","doi-asserted-by":"publisher","DOI":"10.1017\/S0031182000057164"},{"key":"S0031182000066853_ref001","volume-title":"Population Dynamics of Infectious Diseases","author":"Anderson","year":"1982"},{"key":"S0031182000066853_ref003","doi-asserted-by":"publisher","DOI":"10.1080\/00034983.1959.11685912"},{"key":"S0031182000066853_ref004","first-page":"24","volume-title":"Annual Report 1965, East Africa Trypanosomiasis Research Organization","author":"Bailey","year":"1966"},{"key":"S0031182000066853_ref005","volume-title":"The Biomathematics of Malaria","author":"Bailey","year":"1982"},{"key":"S0031182000066853_ref010","volume-title":"Animal Health Yearbook","year":"1982"},{"key":"S0031182000066853_ref012","doi-asserted-by":"publisher","DOI":"10.1093\/jmedent\/19.3.268"},{"key":"S0031182000066853_ref014","doi-asserted-by":"publisher","DOI":"10.1093\/jmedent\/20.6.673"},{"key":"S0031182000066853_ref015","first-page":"199","article-title":"\u00c9cologie des glossines en secteur pr\u00e9-forestier de C\u00f4te d'Ivoire. 4. Dynamique de l'\u00e9codistribution en terroir villageois","volume":"20","author":"Gouteux","year":"1982","journal-title":"Cahiers de l'Office de la Recherche Scientifique et Technique Outre-Mer, S\u00e9rie Entomologie M\u00e9dicale et Parasitologie"},{"key":"S0031182000066853_ref016","first-page":"3","article-title":"\u00c9cologie des glossines en secteur pr\u00e9forestier de C\u00f4te d'Ivoire. 2. Les pr\u00e9f\u00e9rences trophiques de Glossina palpalis s.l","volume":"20","author":"Gouteux","year":"1982","journal-title":"Cahiers de l'Office de la Recherche Scientifique et Technique Outre-Mer, S\u00e9rie Entomologie M\u00e9dicale et Parasitologie"},{"key":"S0031182000066853_ref017","first-page":"109","article-title":"\u00c9cologie des glossines en secteur pr\u00e9forestier de C\u00f4te d'Ivoire. 3. Les pr\u00e9f\u00e9rences trophiques de Glossina pallicera et G. nigrofusca. Comparaison avec G. palpalis et implications \u00e9pid\u00e9miologiques","volume":"20","author":"Gouteux","year":"1982","journal-title":"Cahiers de l'Office de la Recherche Scientifique et Technique Outre-Mer, S\u00e9rie Entomologie M\u00e9dicale et Parasitologie"},{"key":"S0031182000066853_ref019","doi-asserted-by":"publisher","DOI":"10.1016\/0167-5877(83)90018-1"},{"key":"S0031182000066853_ref021","volume-title":"The Trypanosomes of Mammals","author":"Hoare","year":"1972"}],"container-title":["Parasitology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0031182000066853","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,20]],"date-time":"2019-05-20T19:23:35Z","timestamp":1558380215000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0031182000066853\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1988,8]]},"references-count":54,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1988,8]]}},"alternative-id":["S0031182000066853"],"URL":"https:\/\/doi.org\/10.1017\/s0031182000066853","relation":{},"ISSN":["0031-1820","1469-8161"],"issn-type":[{"value":"0031-1820","type":"print"},{"value":"1469-8161","type":"electronic"}],"subject":[],"published":{"date-parts":[[1988,8]]}}}