  We investigate theoretically if treatment alone can reduce the
schistosomiasis's prevalence in an infected population, in a long-lasting
sustainable way. We use a non-linear system of ordinary differential equations
(a SI system combined with a logistic population growth) which describes the
time evolution of the non-infected and infected populations, in terms of the
recovering, infection, and demographic rates.
  Our model leads to the conclusion that the only way to eliminate this endemic
disease is to implement public health policies aimed at both treatment and
environment.
  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\%. The
epidemiological data are extracted from a longitudinal study carried on the
region between 2001 and 2010 and the demographic parameter from official
Brazilian population data. When these estimated parameters are entered, our
model gives a limit prevalence for Virgem das Gra\c{c}as of 11\%, which is
still significantly high even though treatment in accordance to the government
regulations is systematically performed. This estimative reinforces once again,
that in order to eliminate Schistomiasis, public health policies aimed at
treatment, sanitation, including snail control, and health education programs
are mandatory.
