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With the outbreak of COVID-19, great loss and damage were brought to human society, making the study of epidemic spreading become a significant topic nowadays. To analyze the spread of infectious diseases among different areas, e.g., communities, cities, or countries, we construct a network, based on the epidemic model and the network coupling, whose nodes denote areas, and edges represent population migrations between two areas. Each node follows its dynamic, which describes an epidemic spreading among individuals in an area, and the node also interacts with other nodes, which indicates the spreading among different areas. By giving mathematical proof, we deduce that our model has a stable solution despite the network structure. We propose the peak infected ratio (PIR) as a property of infectious diseases in a certain area, which is not independent of the network structure. We find that increasing the population mobility or the disease infectiousness both cause higher peak infected population all over different by simulation. Furthermore, we apply our model to real-world data on COVID-19 and after properly adjusting the parameters of our model, the distribution of the peak infection ratio in different areas can be well fitted.
Network spreading dynamics is a significant issue in network science. Outbreaks of COVID-19 make research on disease transmission even more important and strategies for epidemic prevention are usually proposed from a regional level. Therefore, this paper establishes an epidemic model considering epidemic spreading among areas. In our model, a network is constructed where nodes represent areas, and edges denote migrations between two areas. For each node in the network, there is a dynamic transition among susceptible, infected, and recovered individuals. We give a proof of the stability at the final state of the system and find that the final solution is only related to the infected transition rate and recovery rate. Based on our model, we put forward the peak infected ratio as a significant index to measure the epidemic in different areas and analyze its property by simulation with statistical methods. By changing the structure of the network, we observe different properties of indexes. In addition, the influence of the connection strength of coupling between areas and the infection rate in the Susceptible-Infected-Recovered (SIR) epidemic model on the infected ratio is also investigated. Additionally, we utilize our model to fit epidemical spreading data in the real world.
