The SEIR Dynamic Evolutionary Model with Markov Chains in Hyper Networks

In real life, individuals play an important role in the social networking system. When an epidemic breaks out the individual’s recovery rate depends heavily on the social network in which he or she lives. For this reason, in this paper a nonlinear coupling dynamic model on the hyper network was built. The upper layer is the dynamic social network under the hypernetwork vision, and the lower layer is the physical contact layer. Thus, the dynamic evolutionary coupling mechanism between the social network and epidemic transmission was established. At the same time, this paper deduced the evolution process of the dynamic system according to the Markov chain method. The probability equation of the dynamic evolution process was determined, and the threshold of epidemic spread on the non-uniform network was obtained. In addition, numerical simulations verified the correctness of the theory and the validity of the model. The results show that an individual’s recovery state will be affected by the individual’s social ability and the degree of information forgetting. Finally, suitable countermeasures are suggested to suppress the pandemic from spreading in response to the coupling model’s affecting factors.