J . theor . Biol . (1997) 188, 495–506 0022–5193/97/200495 + 12 $25.00/0/jt970479  1997 Academic Press Limited Acquired Immunity on a Schistosomiasis Transmission Model— Fitting The Data H M Y,*† F A B C‡  E M‡ * Universidade Estadual de Campinas , IMECC—Depart . Mat . Aplicada , Caixa Postal 6065, CEP: 13081-970; Campinas , S.P., Brazil ‡ USP—FM, Av . Dr . Arnaldo , 455, S.P., Brazil (Received on 11 November 1995, Accepted in revised form on 16 May 1997) A semi-stochastic model is proposed to analyse the effects of acquired immunity on the transmission of schistosomiasis in the human host. The basic model’s assumptions are as follows. The human host is assumed to build up an immune response after elapsing a fixed period of time L from the first infection. This acquired immunity is assumed to be partially effective and it is never lost. The parasite infection event is a Poisson process with multiple occurrences, i.e., in each event one or more cercaria are assumed to invade the host. The model treats deterministically the age distribution of human host. The model shows a good retrieving capacity of real data from two endemic areas of schistosomiasis: Touros, Brazil (Schistosoma mansoni ) and Misungwi, Tanzania (Schistosoma haematobium).  1997 Academic Press Limited 1. Introduction Schistosomiasis has probably the most complex biological cycle of all human infections, involving at least two host species (human and snail), two free-living transmission stages of the parasite (cercariae and miracidiae) and distinct environments. Humans are the principal, definitive host for the five schistosome species. Adult worms live in the venous system of intestine (Schistosoma mansoni , Schistosoma japonicum, Schistomosa mekongi and Schistomosa intercalatum) or the urinary bladder (Schistosoma haematobium) (Mahmoud, 1990). As a result of the sexual reproduction of the parasite in different human organs, the characteristically shaped eggs pass through the vesical or intestinal wall in order to find their way to outside via the host excreta. In fresh water the eggs hatch and release ciliated, motile miracidia that soon penetrate into the snail (the intermediate host). Inside the snail the miracidia multiply asexually, and in 4–6 weeks hundreds of thousands of motile, forked-tail cercaria emerge. These are the forms infective to the human host. For each species of schistosome and for each geographic region there is a specific snail as the intermediate host. Therefore, it is believed that the geographic distribution of schistosomiasis depends on the distribution of the specific snails. On encountering human skin, the cercaria actively penetrate it, causing a local reaction. In the process of invasion, the cercaria lose their tails and change into schistoso- mula, which then migrate to the lungs and liver; in about 6 weeks they mature to adult worms, mate and descend, via the venous system, to their final habitat. The lifespan of adult worms is still a controversy, ranging from 5–10 years to more than 30 years (Harris et al ., 1984; Vermund et al ., 1983). For mathematical models to be of any use they must be sufficiently realistic and grounded in † Author to whom correspondence should be addressed. E-mail: hyunyangime.unicamp.br.