We propose an autologistic network model on binary spatiotemporal data to study the spreading patterns of disease. The proposed model identifies an underlying network, without the pre-specification of neighborhoods based on proximity, that can have varying effects depending on the previous states. The model parameters are estimated by maximizing the penalized pseudolikelihood with bias-corrected, which can be adapted to the generalized linear model (GLM) framework, where we show the resulting estimators are asymptotically normal. We provide spatial-joint transition probabilities for predicting disease status in the next time interval. Simulation studies were conducted to evaluate the validity and performance of the proposed method. Examples are provided using the amyotrophic lateral sclerosis (ALS) patients’ data from EMPOWER Study.