Multi-Disease Transmission with Coupling and Threshold Perturbations on Hypergraph Structure

In reality, infectious diseases rarely spread in isolation; instead, multiple diseases often spread concurrently. The infection of one disease may influence an individual’s susceptibility or transmissibility of another disease through mechanisms such as immunosuppression or symptom superposition. Furthermore, population contact structures are not limited to simple pairwise interactions, but also involve group events with simultaneous exposure, such as family gatherings. Traditional network models, which are based on pairwise interactions, are difficult to accurately capture these higher-order interaction structures and the coupling mechanisms among multiple pathogens. Therefore, this paper presents a hypergraph SIS transmission model based on dynamic thresholds. It systematically investigates the transmission dynamics of multiple diseases on uniform and non-uniform hypergraph structures in BA and ER networks. According to co-infection scenarios, three coupling mechanisms are proposed, positive coupling which promotes co-infection, negative coupling which suppresses co-infection, and no coupling where transmission occurs independently. To account for variations in initial disease intensity, three comparison groups are designed: high-low, same-high and same-low. This paper analyses the combined effects of coupling mechanisms, threshold variations and network structural characteristics on the transmission thresholds, propagation rates and infection scales of multiple diseases. These findings are validated in a dengue fever transmission network.