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We investigate theoretically if treatment alone can reduce theschistosomiasis's prevalence in an infected population, in a long-lastingsustainable way. We use a non-linear system of ordinary differential equations(a SI system combined with a logistic population growth) which describes thetime evolution of the non-infected and infected populations, in terms of therecovering, infection, and demographic rates.  Our model leads to the conclusion that the only way to eliminate this endemicdisease is to implement public health policies aimed at both treatment andenvironment.  We apply our model to the endemic area of Virgem das Gra\c{c}as, in Brazil,where the prevalence of Schistosiamisis in 2001 was greater than 50\%. Theepidemiological data are extracted from a longitudinal study carried on theregion between 2001 and 2010 and the demographic parameter from officialBrazilian population data. When these estimated parameters are entered, ourmodel gives a limit prevalence for Virgem das Gra\c{c}as of 11\%, which isstill significantly high even though treatment in accordance to the governmentregulations is systematically performed. This estimative reinforces once again,that in order to eliminate Schistomiasis, public health policies aimed attreatment, sanitation, including snail control, and health education programsare mandatory.

Modeling the prevalence of Schistosoma mansoni infection in an endemic population