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.