Numerical simulation of a SIS epidemic model based on a nonlinear Volterra integral equation

We consider a SIS epidemic model based on a Volterra integral equation and we compare the dynamical behavior of the analytical solution and its numerical approximation obtained by direct quadrature methods. We prove that, under suitable assumptions, the numerical scheme preserves the qualitative properties of the continuous equation and we show that, as the stepsize tends to zero, the numerical bifurcation points tend to the continuous one.