Abstract: Addressing at the general characteristics of random fluctuations in the propagation process,by uniforming network SIRS model for research object,the paper established a random network model based on continuous time Markovchain,and it analyzed the steady-state threshold and critical conditions of random network model.The conclusion of random network model is the same with the result of the mean-field approach．In addition,Propagation model was established based on continuous time Markov chain,in the description of the phenomenon of random fluctuations in the propagation process,the theory explained were given better than the mean-field approach,which is the most obvious advantage compared with the mean-field method in resolving such problems.As well as the paper provided an analysis of the behavior of the transmission dynamics of complex networks of ideas based on probability and statistics methods.

Key words: Random fluctuation,Continuous time markov chain,Complex-network,SIRS propagation model,Steady-state distribution