Until recently, almost all studies of leishmaniasis epidemiology were qualitative and descriptive. But now that the natural history of many Leishmania parasites is quite well known, there is growing interest in quantitative analysis. In this paper I use mathematical models in conjunction with field data to try to answer a wider range of questions than has previously been possible with descriptive techniques, and to sharpen some of the outstanding questions for laboratory workers. This is done with reference to the persistence and resilience of canine leishmaniasis, the maintenance of virulence poly morphisms in Leishmania populations, and the possible existence of cycles of human kala-azar. I conclude by posing a set of problems under three headings: diagnosis of infection (as distinct from disease), natural immunity to Leishmania infection in the vertebrate host, and genetic variation in the parasite population. Some solutions from the laboratory can be found in the companion paper by Black (1992).
