Journal of Biological Systems, Vol. 17, No. 3 (2009) 397–423 c  World Scientific Publishing Company MATHEMATICAL ANALYSIS OF THE TRANSMISSION DYNAMICS OF SCHISTOSOMIASIS IN THE HUMAN-SNAIL HOSTS EDWARD T. CHIYAKA Modeling Biomedical Systems Research Group c/o Department of Applied Mathematics National University of Science and Technology P. O. Box AC 939 Ascot, Bulawayo, Zimbabwe Center of Excellence in Epidemiological Modeling and Analysis Stellenbosch University, c/o STIAS 19 Jonkershoekweg, Stellenbosch 7600 Capetown, South Africa echiyaka@nust.ac.zw WINSTON GARIRA Department of Mathematics and Applied Mathematics University of Venda, Private Bag X5050 Thohoyandou 0960, South Africa winston.garira@univen.ac.za Received 29 July 2008 Accepted 9 January 2009 The spread and persistence of schistosomiasis are some of the more complex host parasite processes to model mathematically because of the different larval forms assumed by the parasite and the requirement of two hosts during the life cycle. We construct a determin- istic mathematical model to study the transmission dynamics of schistosomiasis where the miracidia and cercariae dynamics are incorporated. The model is analyzed to gain insights into the qualitative features of the equilibrium which allows the determination of the basic reproductive number. Conditions for existence of the endemic equilibrium are discussed and its local stability is determined using the Center Manifold Theory. Analytical and numerical techniques are employed to assess the conditions of contain- ment and persistence of schistosomiasis. Our results show that control strategies that target the transmission of the disease from the snail to man will be more effective in the control of the disease than those that block the transmission from man to snail. Keywords : Schistosomiasis; Biomphalaria glabrata; Center Manifold; Mathematical Modeling. 1. Introduction Schistosomiasis, also referred to as bilharzia, bilharziasis and snail fever, is a par- asitic disease that was first described by Theodor Bilharz in 1851, after whom the disease was initially named bilharzia. 1 It is prevalent in many parts of the devel- oping world, particularly Africa, South America, and Asia, with an estimated 650 397