The Influence of Vaccine Willingness on Epidemic Spreading in Social Networks

The vaccination has played a significant role in government departments to control the spread of infectious diseases. Therefore, it is interesting to theoretically analyse the impact of vaccination on the disease spreading. In this article, we propose a discrete-time epidemic-willingness dynamics model to analyse the influence of vaccine willingness on epidemic spreading. Sufficient conditions are provided to guarantee that the proportion of the infected population exponentially converges to zero. The explicit relationship between the trend of epidemic spreading and the willingness-based reproduction number is presented. Based on the real data from a survey conducted on a sample of Italian population, we employ the proposed epidemic-willingness dynamics model to reproduce the social phenomenon that increasing the willingness to vaccinate can reduce and delay the maximum proportion of infected communities. Additionally, simulation experiments validate the effectiveness of the proposed epidemic-willingness dynamics model by utilizing the real data of COVID-19 infections from 28 February to 31 May 2022 in Shanghai. It is shown that the higher the level of infection, the greater the willingness to vaccinate. Moreover, we find that the willingness-based reproduction number is not monotonically decreasing and differs from the classical reproduction number.