This paper develops and implements a World Wide Web cache infrastructure model which is to be used for analysis of features that are otherwise difficult to get from existing log data or for evaluation of nonexisting cache scenarios. A prominent feature of our model that differentiates it from other similar models is its dynamical aspect, which allows for the investigation of temporal features. Using the model we verify and quantify an observation made from real log data that the popularity of Web pages diversifies the higher we go in the cache hierarchy. We then use the model to predict the cache population dynamics in a hypothetical scenario of sufficiently large caches.