Analysis of the epidemic vaccination evolution through the K-shell decomposition method

Recently, the novel coronavirus (SARS-CoV-2) has been raging around the world. Vaccination is currently the most effective way to control the spread of infectious diseases. In this paper, an epidemic vaccination model based on k-shell decomposition method is established to analyze the influence of vaccination on the spread of infectious diseases from the perspectives of mandatory vaccination and voluntary vaccination. For the compulsory vaccination strategy, the importance of the nodes in the network is sorted by the k-shell decomposition method. And the nodes with greater node importance are forced to be vaccinated. For the voluntary vaccination strategy, the influence of the initially vaccinated node on the remaining nodes is analyzed based on the evolutionary game model. Finally, the numerical simulation experiments are carried out using the USAir network and the Facebook network. The results show that compared to the mandatory vaccination strategy, the voluntary vaccination strategy can achieve a smaller epidemic size when the core number vaccinated is equal. For the Facebook network, vaccinated nodes in the lower layer instead of the higher layer can yield a smaller epidemic size if vaccination is carried out by layer.