Fractional Derivatives in Dengue Epidemics

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.