Epidemic Spreading and Control on Preferential Attachment Hypergraph with Community

Contagion backbone of temporal higher-order networks

Temporal higher-order networks, where each hyperlink involving a group of nodes is activated or deactivated over time, effectively represent social interactions. They serve as substrates for the spread of epidemics and information. However, the contribution of each hyperlink to a contagion process, namely, the average number of nodes that are infected via its activation, and the network properties of hyperlinks that influence this contribution, remain unexplored. Here we show, for the Susceptible-Infectious threshold process on temporal higher-order networks derived from human face-to-face interactions, that the contribution of each hyperlink can be quantified by a contagion backbone, whose dependency on the diffusion parameters is demonstrated and supported by theoretical analysis. We design centrality metrics of hyperlinks to estimate hyperlink rankings based on their contributions, revealing that local properties of hyperlinks can effectively identify high-contributing hyperlinks, and explain why different centrality metrics perform better under different process parameters. These insights are crucial for designing effective interventions that mitigate the spread of epidemics or misinformation.

Extreme outbreaks in non-Markovian epidemics on complex networks

Extreme epidemic risk is controlled by the right tail of the outbreak-size distribution, but this distribution is generally unknown for non-Markovian spreading on networks. Here we determine this distribution by mapping non-Markovian SIR dynamics to an effective Markovian description. We show that arbitrary infection and recovery time statistics can be incorporated through a single edge transmissibility, yielding an effective Markovian process that reproduces the full outbreak-size statistics. For weakly heterogeneous networks, the reduction yields a universal well-mixed semiclassical theory governed by the bond-percolation reproductive number. Outbreak statistics across diverse waiting-time distributions and topologies collapse onto one predictive curve. For highly heterogeneous and empirical networks, the corresponding effective Markovian dynamics on the network captures the complete distribution. Our results provide a direct route from measured waiting-time distributions to quantitative predictions of network-level extreme-outbreak risk.

Turing instability and bistable epidemic spread on complex networks: Effects of topology and initial seeding.

Understanding how diseases propagate through structured populations is essential for predicting and controlling epidemics. This study develops a reaction-diffusion framework on complex networks to investigate how local bistability, dispersal, and network topology jointly determine infection dynamics. Analytical conditions for Turing instability are derived and examined in Erdős-Rényi and scale-free networks using a bistable susceptible-infected model under mean-field approximation. The analysis shows that high-degree nodes become monostable, whereas low and intermediate-degree nodes exhibit bistability. Simulations confirm that infection outcomes depend strongly on degree distribution, transmission rate, and dispersal intensity. Epidemics seeded at highly connected nodes spread faster and more extensively, while structural differences between network types yield distinct thresholds and outbreak patterns. Together, these results reveal how local nonlinearities and network heterogeneity interact to shape epidemic transitions, offering a theoretical basis for understanding spatial disease persistence and designing targeted control strategies.

Dynamics of pairwise-based SIS epidemic models on clustered networks with higher-order interactions

Epidemic Processes in Networks: A Comprehensive Study of SIR Model and Network Topologies

In this paper, we explore the dynamics of epidemic processes on different types of single-layer network structures, emphasizing the impact of network structure on the spread of disease. We first propose a single-layer SIR (susceptible-infected-recovered) network model and investigate the impact of network structure on virus transmission. Numerical simulation results indicate that in scale-free networks, infections in hub nodes lead to faster and more widespread spread compared to the absence of such a network. In terms of epidemic control, the importance of disconnecting key nodes is emphasized. In random networks, transmission is generally faster and has higher peak infection levels than in scale-free networks. The findings reveal that network topology and initial infection nodes profoundly influence virus spread patterns, offering critical insights for designing targeted epidemic control strategies that minimize transmission by breaking key network links.

Traffic-driven sequential spread of two interacting epidemics on complex networks.

While the coupling between traffic dynamics and epidemic spreading on complex networks has been widely studied, existing research has predominantly focused on single-pathogen transmission. In this paper, we investigate the sequential spreading dynamics of two interacting epidemics driven by traffic flow. The model incorporates a key mechanism whereby prior infection with the first disease alters a node's susceptibility to the second disease. We develop a heterogeneous mean-field framework for the coupled spreading process and derive analytical expressions for the epidemic thresholds. Our results show that the interaction parameter α and the infection rate of the first epidemic β1 jointly determine the outbreak threshold and stationary prevalence of the second epidemic. The parameter α regulates how prior infection influences susceptibility to the second epidemic, ranging from suppressive interaction (α < 1) through neutral interaction (α = 1) to synergistic interaction (α > 1). A pronounced nonlinear threshold response emerges: in the suppressive interaction regime, increasing β1 below its critical point substantially raises the epidemic threshold of the second disease, whereas in the synergistic interaction regime, it lowers the threshold. Once the first epidemic exceeds its critical point, both effects gradually saturate. Numerical simulations show good agreement with the theoretical predictions and further demonstrate the robustness of the results across different network sizes and average degrees. These findings reveal how epidemic interactions and network structure jointly shape sequential spreading dynamics in traffic-driven systems, providing new insights into coupled contagion processes on complex networks.