Analysis of SIS epidemic model in bi-uniform hypernetworks

To describe the dynamics of epidemic spread with multiple individuals interacting with each other, we develop a susceptible-infected-susceptible (SIS) spread model with collective and individual contagion in general hypernetworks with higher-order interactions. The constructed model is applied to a bi-uniform hypernetwork to obtain a mean-field model for the SIS model. The threshold value at which an epidemic can spread in the bi-uniform hypernetwork is obtained and analyzed dynamically. By analysis, the model leads to bistability, in which a disease-free equilibrium and an endemic equilibrium coexist. Finally, numerical simulations of the developed model are carried out to give the effect of the proportion of individual contagion hyperedges on the spread of an epidemic.