In this paper, we study a dynamically consistent numerical method for the approximation of a nonlinear integro-differential equation modeling an epidemic with age of infection. The discrete scheme is based on direct quadrature methods with Gregory convolution weights and preserves, with no restrictive conditions on the step-length of integration h, some of the essential properties of the continuous system. In particular, the numerical solution is positive and bounded and, in cases of interest in applications, it is monotone.

For the finite weighted Hilbert transform we consider two different product integration rules, the VP rule and the L-rule, based on the same nodes and obtained by approximating the density function with filtered de la Vallée Poussin and classical Lagrange interpolation polynomials, respectively. The L-rule is well known and widely studied.

According to the European Charter for Researchers «all researchers should ensure [...] that the results of their research are disseminated and exploited, e.g. communicated, transferred into other research settings or, if appropriate, commercialised ...». Therefore, it's part of the researchers' mission to raise the general public awareness with respect to science. This need is further emphasized by a survey of Eurobarometer 2010: society is strongly interested in science but, at the same time, is often scared by the risks connected with new technologies.