Higher-Order Co-Infection on Hypergraphs

People encounter infections through overlapping groups, such as households, classrooms, and workplaces. Understanding how these shared contacts affect the spread of multiple pathogens is critical to determining what information epidemic models need to retain. We introduce HyCo-SIS (Higher-order Co-infection SIS), a discrete-time SIS model on hypergraphs with explicit reinforcement between overlapping active groups and pairwise transmission. We investigate how this reinforcement affects infection dynamics and whether simplified representations of hypergraphs preserve the resulting behavior. We derive an exact representation of overlap reinforcement as target-dependent four-person interactions and determine when a symmetric representation is possible. Numerical experiments examine reinforcement strength, contact structure, and susceptibility to secondary infection, as well as calibrated pairwise approximations. Our results demonstrate that redistributing overlap weights can substantially change finite-time co-infection even when every individual's total overlap coefficient is preserved. We further derive an exact five-person calculation and demonstrate why equal mean infection pressure does not necessarily produce equal acquisition probabilities. These findings identify how the allocation of higher-order interactions can influence contagion dynamics beyond their aggregate strength. Beyond epidemiology, this work contributes to the statistical physics of spreading processes by examining how the arrangement of many-body interactions shapes collective dynamics, and what information is lost when those interactions are simplified.