Severe Acute Respiratory Syndrome (SARS), the first epidemic of the 21st century, has an outbreak history of more than 2 years till today and caused tremendous damage to the human society. Accordingly, many studies on modeling the SARS epidemic have been reported, whereas deficiencies were still lying in those models because of their separate space/time methodology. In this paper, we propose novel comprehensive stochastic spatio-temporal models from both of the macro aspect and individual aspect for characterizing transmission and control of the SARS disease. Based on a new SARS spread process in consideration of "suspicious" population, we firstly establish the stochastic temporal models from two different aspects: the macro model is described with birth-death process and the individual Markov model is described with probability transition matrix (PTM). And then, we amalgamate the deterministic/stochastic population-flow model with the stochastic temporal models together to set up the comprehensive stochastic spatio-temporal models. Simulations on computer have evaluated the effect of various realistic parameters and control policies, and also have testified the accuracy and efficacy of the new models. Additionally, particular studies on the cases of Tsinghua University and Beijing City are presented. The comprehensive stochastic spatio-temporal models have considerably reduced the complexity plus errors as compared with previous works and will be able to characterize other various epidemics, e.g. Avian Flu.
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