  We introduce the use of fractional calculus, i.e., the use of integrals and
derivatives of non-integer (arbitrary) order, in epidemiology. The proposed
approach is illustrated with an outbreak of dengue disease, which is motivated
by the first dengue epidemic ever recorded in the Cape Verde islands off the
coast of west Africa, in 2009. Numerical simulations show that in some cases
the fractional models fit better the reality when compared with the standard
differential models. The classical results are obtained as particular cases by
considering the order of the derivatives to take an integer value.
