Multigroup SEIV Epidemics on Hypergraph

Hypergraph has successfully addressed the limitations of conventional graph in describing group interactions in social networks and the spread of infectious diseases. However, the effects of implementing vigilance measures in the context of group interactions have not been fully studied. Therefore, this paper studies a higher-order Susceptible-Exposed-Infected-Vigilant (SEIV) compartmental model incorporating vigilance measures and explores its evolution process on a hypergraph. In this model, a fraction of individuals remain vigilant either after infection or in general due to their alertness to disease transmission. By using the mean field method and tensor algebra, we derived the conditions for the existence of disease-free equilibrium and endemic equilibrium and their stability. Numerical simulation results also show that due to group interactions, bistable phenomena may occur.