时间连续马尔可夫链的复杂网络上SIRS模型分析

SIRS Model on Complex Network of Continuous Time Markov Chain Based on Analysis

针对传播过程中普遍存在的随机波动特点,以均匀网络上的基本SIRS模型为研究对象,建立基于时间连续马尔可夫链的随机网络模型,以平稳分布为研究方法分析了模型的稳态阈值和临界条件,发现所得结果和采用平均场方法所得结果相同;而基于时间连续马尔可夫链建立的传播模型,在对传播过程中存在的随机波动现象的描述方面,给出了较充分的理论解释,这也是概率统计方法在解决此类问题上较平均场方法最明显的优势所在,同时也为分析复杂网络上的传播动力学行为提供了一种基于概率统计方法的思路。

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 Markov chain, 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.