Analysis of the SEIR mean-field model in dynamic networks under intervention

For emerging respiratory infectious diseases like COVID-19, non-pharmaceutical interventions such as isolation are crucial for controlling the spread. From the perspective of network transmission, non-pharmaceutical interventions like isolation alter the degree distribution and other topological structures of the network, thereby controlling the spread of the infectious disease. In this paper, we establish a SEIR mean-field propagation dynamics model for the synchronous evolution of dynamic networks caused by propagation and tracing isolation. We employ the reducing-dimension method to convert the mean-field model in networks into an equivalent and simpler low-dimension model, and then calculate the exact expression of the final size. In addition, we get the differential equations of the degree distribution over time in dynamic networks under tracing isolation and the relationships between the first and second moment of the dynamic network. While the degree of a node remains constant regardless of its state in many previous studies, this paper takes into account that the degree of each node changes over time whatever its state under the disease spread and intervention measures.