  Dengue is a vector-borne disease transmitted from an infected human to an
Aedes mosquito, during a blood-meal. Dengue is still a major public health
problem. A model for the disease transmission is presented, composed by human
and mosquitoes compartments. The aim is to simulate the effects of seasonality,
on the vectorial capacity and, consequently, on the disease development. Using
entomological information about the mosquito behavior under different
temperatures and rainfall, simulations are carried out and the repercussions
analyzed. The basic reproduction number of the model is given, as well as a
sensitivity analysis of model's parameters. Finally, an optimal control problem
is proposed and solved, illustrating the difficulty of making a trade-off
between reduction of infected individuals and costs with insecticide.
