Epidemic spreading on biological evolution networks

Abstract

The spread of epidemics is closely related to network structure. In reality, network structure will change over time with the departure or employment of many individuals. Mathematical models can not only be used to simulate the evolution of networks, but also to better analyze the changes in the spread of epidemics. In the present work, we propose two mathematical models of evolution networks with the addition and deletion of nodes to analyze epidemic spread on homogeneous and heterogeneous networks. We discuss various factors affecting the spread of epidemics when the evolution network reaches a steady state, including the number of new nodes and their initial degree, the deletion rate of nodes, and so on. The results show that in homogeneous networks, the epidemic threshold first increases and then decreases, while in heterogeneous networks, the epidemic threshold increases or decreases under certain conditions. It provides many measures to improve the epidemic threshold and slow down the spread of epidemics.