Kuniya Toshikazu
1-1 Rokkodai-cho, Nada-ku, Kobe, 657-8501 Japan.
Jpn Econ Rev (Oxf). 2021;72(4):581-607. doi: 10.1007/s42973-021-00094-8. Epub 2021 Aug 31.
In this paper, we review the structure of various epidemic models in mathematical epidemiology for the future applications in economics. The heterogeneity of population and the generalization of nonlinear terms play important roles in making more elaborate and realistic models. The basic, effective, control and type reproduction numbers have been used to estimate the intensity of epidemic, to evaluate the effectiveness of interventions and to design appropriate interventions. The advanced epidemic models includes the age structure, seasonality, spatial diffusion, mutation and reinfection, and the theory of reproduction numbers has been generalized to them. In particular, the existence of sustained periodic solutions has attracted much interest because they can explain the recurrent waves of epidemic. Although the theory of epidemic models has been developed in decades and the development has been accelerated through COVID-19, it is still difficult to completely answer the uncertainty problem of epidemic models. We would have to mind that there is no single model that can solve all questions and build a scientific attitude to comprehensively understand the results obtained by various researchers from different backgrounds.
在本文中，我们回顾了数学流行病学中各种流行病模型的结构，以便未来在经济学中应用。人口的异质性和非线性项的推广在构建更精细、更现实的模型中起着重要作用。基本再生数、有效再生数、控制再生数和类型再生数已被用于估计疫情的强度、评估干预措施的有效性以及设计适当的干预措施。先进的流行病模型包括年龄结构、季节性、空间扩散、突变和再感染，并且再生数理论也已推广到这些模型中。特别地，持续周期解的存在引起了人们的极大兴趣，因为它们可以解释疫情的反复波动。尽管流行病模型理论已经发展了几十年，并且通过新冠疫情其发展得到了加速，但仍然难以完全回答流行病模型的不确定性问题。我们必须牢记，没有一个单一的模型能够解决所有问题，并且要树立科学的态度，以全面理解来自不同背景的各种研究人员所获得的结果。
