Although microscopic models are nowadays getting more and more popular among, still the model-ling approach lacks of appropriate mathematical theory to confidentally rely on the outputs of the derived mod-els. Especially unexpected chaotic group behaviour and the inability to validate and parametrise the model often leads to unusable simulations. The investigated test-case, a simple cellular automaton (CA) simulating the temporal development of a SIR (Susceptible-Infected-Recovered) type epidemic, shows a field of application for so called complexity theory. In order to explain and analyse the aggregated simulation results of the CA, certain methods usually used in Markov theory for quan-tum mechanics, basically extensions of so called diffusion approximation, are applied. Finally, already suspected, correlations to the solutions of the famous SIR differential equations, formerly derived by Kermack and McKendrick, can be proven with analytical methods and extended by convergence results and qualitative error estimations.