  In this work we propose a model that represents the relation between fish
ponds, the mosquito population and the transmission of malaria.
  It has been observed that in the Amazonic region of Acre, in the North of
Brazil, fish farming is correlated to the transmission of malaria when carried
out in artificial ponds that become breeding sites. Evidence has been found
indicating that cleaning the vegetation from the edges of the crop tanks helps
to control the size of the mosquito population.
  We use our model to determine the effective contribution of fish farming
practices on malaria transmission dynamics. The model consists of a nonlinear
system of ordinary differential equations with jumps at the cleaning time,
which act as impulsive controls. We study the asymptotic behaviour of the
system in function of the intensity and periodicity of the cleaning, and the
value of the parameters. In particular, we state sufficient conditions under
which the mosquito population is eliminated or persists, and under which the
malaria is eliminated or becomes endemic. We prove our conditions by applying
results for cooperative systems with concave nonlinearities.
