The development of vector-transmitted disease models and their application to field studies is reviewed. The key concepts of the basic rate of reproduction and disease transmission threshold are explained, and their application to disease control briefly illustrated. The complications involved in producing appropriate models are discussed for the case of the trypanosomatid parasites
Leishmania
and
Trypanosoma
that frequently have more than one vertebrate host and are often fatal in the human host. A two-species, vector-borne disease model allows a quantification of the role of animal reservoirs in maintaining human diseases. Human prevalence may be determined more by the parasitological characteristics of wild reservoir species, about which little is generally known, than by any other single feature of the complex interaction between parasites, vectors and hosts. Domestic animals are often ideal reservoirs, maintaining large numbers of vectors and considerably enlarging the parasite pool. When vector-transmitted diseases are fatal to the human host, human and vector dynamics interact in ways which may cause epidemic cycles, low-level endemic equilibria or disease extinction. For both leishmaniasis and trypanosomiasis it is suggested that a very small number of chronic human cases can maintain the disease in the human population over long periods of time between epidemic outbreaks. They may also be important in the maintenance of geographically distinct foci, characteristic of human trypanosomiasis in Africa. Finally there is a plea to establish a tradition of field observation leading to, and being directed by, mathematical models which in turn are modified as the observations accumulate. All too often, one-way traffic between the two results in slow, or misguided, progress.
Dynamics of a delayed plant disease model with Beddington-DeAngelis disease transmission