School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, People's Republic of China.
Chaos. 2021 Jan;31(1):013102. doi: 10.1063/5.0019995.
The study of epidemics spreading with community structure has become a hot topic. The classic SIR epidemic model does not distinguish between dead and recovered individuals. It is inappropriate to classify dead individuals as recovered individuals because the real-world epidemic spread processes show different recovery rates and death rates in different communities. In the present work, a SIRD epidemic model with different recovery rates is proposed. We pay more attention to the changes in the number of dead individuals. The basic reproductive number is obtained. The stationary solutions of a disease-free state and an endemic state are given. We show that quarantining communities can decrease the basic reproductive number, and the total number of dead individuals decreases in a disease-free steady state with an increase in the number of quarantined communities. The most effective quarantining strategy is to preferentially quarantine some communities/cities with a greater population size and a fraction of initially infected individuals. Furthermore, we show that the population flows from a low recovery rate and high population density community/city/country to some high recovery rate and low population density communities/cities/countries, which helps to reduce the total number of dead individuals and prevent the prevalence of epidemics. The numerical simulations on the real-world network and the synthetic network further support our conclusions.
具有社区结构的传染病传播研究已成为热点。经典的 SIR 传染病模型不区分死亡和康复个体。将死亡个体归类为康复个体是不合适的，因为现实世界中的传染病传播过程在不同社区中表现出不同的康复率和死亡率。在本工作中，提出了一种具有不同康复率的 SIRD 传染病模型。我们更加关注死亡个体数量的变化。得到了基本再生数。给出了无病状态和地方病状态的稳定解。我们表明，对社区进行隔离可以降低基本再生数，并且随着隔离社区数量的增加，无病稳定状态下的死亡个体总数减少。最有效的隔离策略是优先隔离一些人口规模较大且初始感染个体比例较高的社区/城市。此外，我们表明，人口从低康复率和高人口密度社区/城市/国家流向一些高康复率和低人口密度的社区/城市/国家，这有助于减少死亡个体总数并防止传染病流行。对真实网络和合成网络的数值模拟进一步支持了我们的结论。
