title: Dynamics of a delay Schistosomiasis model in snail infections.
abstract: In this paper we modify and study a system of delay differential equations model proposed by Nasell and Hirsch (1973) for the transmission dynamics of schistosomiasis. The modified stochastic version of MacDonald's model takes into account the time delay for the transmission of infection. We carry out bifurcation studies of the model. The saddle-node bifurcation of the model suggests that the transmission and spread of schistosomiasis is initial size dependent. The existence of a Hopf bifurcation due to the delay indicates that the transmission can be periodic.
authors.affiliation: Department of Mathematics and Statistics, LAMPS and CDM, York University, Toronto, Ontario, Canada. schunhua@mathstat.yorku.ca
authors.forename: Chunhua
authors.initials: C
authors.lastname: Shan
authors.forename: Hongjun
authors.initials: H
authors.lastname: Gao
authors.forename: Huaiping
authors.initials: H
authors.lastname: Zhu
mesh_terms: D000818:Animals; D003198:Computer Simulation; D006801:Humans; D018448:Models, Immunological; D012547:Schistosoma / Q000276:immunology*; D012552:Schistosomiasis / Q000276:immunology* / Q000635:transmission; D012908:Snails / Q000276:immunology* / Q000469:parasitology*; D013269:Stochastic Processes