Spatial autocorrelation is captured using Moran's index. The later quantifies the degree of dispersion (or spread) of events or objects in space. When investigating data in an area, a single Moran statistic may not give a sufficient summary of the autocorrelation spread. However, by partitioning the area and taking the Moran statistics of the subareas, patterns of the local neighbors not otherwise apparent are discovered. We consider the model of the spread of an infectious disease, incorporate time factor, and simulate a multilevel Poisson process where the dependence among the levels is captured by the rate of increase of the disease spread over time, steered by a common factor in the scale. The main consequence of our results is that our Moran statistic is calculated from an explicit algorithm in a Monte Carlo simulation setting. Results are compared to Geary's statistics and estimates of parameters under Poisson process are given.