Positive Numerical Approximation of Integro-Differential Epidemic Model

In this paper, we study a dynamically consistent numerical method for the approximationof a nonlinear integro-differential equation modeling an epidemic with age of infection. The discretescheme 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 ofthe continuous system. In particular, the numerical solution is positive and bounded and, in casesof interest in applications, it is monotone. We prove an order of convergence theorem and show bynumerical experiments that the discrete final size tends to its continuous equivalent as h tends to zero.