  In this paper we propose some mathematical models for the transmission of
dengue using a system of reaction-diffusion equations. The mosquitoes are
divided into infected, uninfected and aquatic subpopulations, while the humans,
which are divided into susceptible, infected and recovered, are considered
homogeneously distributed in space and with a constant total population. We
find Lie point symmetries of the models and we study theirs temporal dynamics,
which provides us the regions of stability and instability, depending on the
values of the basic offspring and the basic reproduction numbers. Also, we
calculate the possible values of the wave speed for the mosquitoes invasion and
dengue spread and compare them with those found in the literature.
