A discussion on mathematical modelling with fractional derivatives with a focus on a SIS epidemiological model

Due to their nonlocal properties, fractional derivatives, such as the Riemann-Liouville or Caputo type, are sometimes used to model memory effects. While their physical interpretation is still not clear, fractional models seem to better describe experimental data, as compared to classical ones. During this talk we will discuss advantages and disadvantages of modelling with fractional derivatives.

As an example, we will consider a SIS epidemiological model and some of its possible fractional generalisations, discussing how the introduction of fractional derivatives might alter the epidemic dynamics.