Voluntary vaccination on hypergraph

Abstract

In reality, when epidemics spread, higher-order interactions in group settings such as homes and schools, for example, can make infections more likely to occur. People often voluntarily get vaccinated to protect themselves and other members of their group from infection. On the other hand, there are individuals who want to “free-ride” and try to avoid infection through herd immunization. Thus, it is clear that vaccination is influenced by both individuals and groups. However, in existing studies, vaccination behavior is often determined only by individual’s self-payoff, with little consideration of group influences. Here, we propose a model of vaccination on a hypergraph. In our model, self-payoff and group-payoff together influence the vaccination. Evolutionary game theory is used to explore the differences in individual vaccination behavior when group-payoff are prioritized versus self-payoff are prioritized. The mean-field method is utilized for theoretical analysis. The experimental results show that at low adoption strength, vaccine cost determines vaccination. When adoption strength is high, priority is given to group-payoff to promote vaccination. If individuals place a extremely high value on self-payoff and have a high strength of adoption, they only vaccinate when the cost of vaccination is as low as zero. Yet, after the rates of infection is high enough, individuals choose to get vaccinated regardless of whether they care more about self-payoff or group-payoff.