In some important biological phenomena Volterra integral and integro-differential equations represent an appropriate mathematical model for the description of the dynamics involved. In the simulation of these real-life problems, numerical solutions should mirror the characteristic physical properties of the original system and maintain accuracy over long-time simulations. We follow this approach to construct and analyze numerical approximations in two cases of interest.
Namely, integral epidemic models structured by age of infection and integro-differential equations for systems of interacting particles. The results are generalized to wider classes of problems.