Effects of network community quarantine strength on disease transmission

Network structural patterns significantly influence the spread of diseases. Real-world networks are not only time-varying in structure but also exhibit varying degrees of community organization. Based on the classical activity-driven network framework, the susceptible-infected-susceptible disease transmission model, and a community-structured network, this paper proposes a novel edge-activity-driven community network model for disease spread by defining an edge activity rate. First, using an improved micro-Markov chain approach, we derive the theoretical epidemic threshold for disease propagation. Under certain conditions, we further solve and analyze the epidemic threshold analytically. Numerical simulations confirm the accuracy of the theoretical approach. Second, extensive numerical experiments reveal that a higher degree of community structure-achieved by reducing inter-community connections while strengthening intra-community links-leads to a larger epidemic threshold. Moreover, the degree of community structure shows an approximately linear negative correlation with the standard deviation of the epidemic threshold. Interestingly, we find that when individuals tend to interact predominantly within their own communities, the final outbreak size decreases. This suggests that during disease outbreaks, implementing strict community-level containment measures can effectively curb the spread of infectious diseases.