Epidemic diffusion is a space-time process, and showing time-series disease maps is a common way to demonstrate an epidemic progression in time and space. Previous studies used time-series maps to demonstrate the animation of diffusion process. Epidemic diffusion patterns were determined subjectively by visual inspection, however. There currently are still methodological concerns in developing effective analytical approaches for profiling diffusion dynamics of disease clustering and epidemic propagation. The objective of this study is to develop a geocomputational algorithm, the modified space-time density-based spatial clustering of application with noise (MST-DBSCAN), for detecting, identifying, and visualizing disease cluster evolution, which takes the effect of the incubation period into account. We also map the MST-DBSCAN algorithm output to visualize the diffusion process. Dengue fever case data from 2014 were used as an illustrative case study. Our results show that compared to kernel-smoothed mapping, the MST-DBSCAN algorithm can better identify the evolution type of any cluster at any epoch. Furthermore, using only one two-dimensional map (and graphs), our approach can demonstrate the same diffusion process that time-series maps or three-dimensional space-time kernel plotting displays but in an easy-to-read manner. We conclude that our MST-DBSCAN algorithm can profile the spatial pattern of epidemic diffusion in detail by identifying disease cluster evolution.