Age structured populations with history dependent mortality and natality

We consider a modification of the Gurtin-MacCamy model of population dynamics, where the birth and death moduli depend on a time integral of the solution rather than on an age integral. This models the influence of past history in the time dependence of the death and birth rates. We propose a numerical algorithm to approximate the solution based on the finite difference method of characteristics and prove that it is optimally convergent. The algorithm is devised to minimize the storage requirement in the time variable.