Fractional derivatives in Dengue epidemics

TL;DR

This paper explores the application of fractional calculus to epidemiological modeling of dengue outbreaks, demonstrating improved fit to real data compared to traditional models, with classical results as special cases.

Contribution

It introduces fractional derivatives into dengue epidemic models, providing a novel approach that enhances modeling accuracy over standard differential equations.

Findings

Fractional models fit dengue outbreak data better than classical models.

Numerical simulations validate the improved accuracy of fractional calculus models.

Classical models are recovered as special cases when derivatives are integer order.

Abstract

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.