This paper presents a model for the efficient and accurate simulations of laminar diffusion-based complex electrokinetic passive micromixers by representing them as a system of mixing elements of relatively simple geometry. Parameterized and analytical models for such elements are obtained, which hold for general sample concentration profiles and arbitrary flow ratios at the element inlet. A lumped-parameter and system-level model is constructed for a complex micromixer, in which the constituent mixing elements are represented by element models, in such a way that an appropriate set of parameters are continuous at the interface between each pair of adjacent elements. The system-level model, which simultaneously computes electric circuitry and sample concentration distributions in the entire micromixer, agrees with numerical and experimental results, and offers orders-of-magnitude improvements in computational efficiency over full numerical simulations. The efficiency and usefulness of the model is demonstrated by exploring a number of laminar diffusion based mixers and mixing networks that occur in practice.