Chen Yuli, Liu Fawang, Yu Qiang, Li Tianzeng
Fuzhou University Zhicheng College, Fujian 350001, China.
School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, QLD 4001, Australia.
Appl Math Model. 2021 Sep;97:281-307. doi: 10.1016/j.apm.2021.03.044. Epub 2021 Apr 20.
The global impact of corona virus (COVID-19) has been profound, and the public health threat it represents is the most serious seen in a respiratory virus since the 1918 influenza A(H1N1) pandemic. In this paper, we have focused on reviewing the results of epidemiological modelling especially the fractional epidemic model and summarized different types of fractional epidemic models including fractional Susceptible-Infective-Recovered (SIR), Susceptible-Exposed-Infective-Recovered (SEIR), Susceptible-Exposed-Infective-Asymptomatic-Recovered (SEIAR) models and so on. Furthermore, we propose a general fractional SEIAR model in the case of single-term and multi-term fractional differential equations. A feasible and reliable parameter estimation method based on modified hybrid Nelder-Mead simplex search and particle swarm optimisation is also presented to fit the real data using fractional SEIAR model. The effective methods to solve the fractional epidemic models we introduced construct a simple and effective analytical technique that can be easily extended and applied to other fractional models, and can help guide the concerned bodies in preventing or controlling, even predicting the infectious disease outbreaks.
冠状病毒（COVID-19）的全球影响深远，其构成的公共卫生威胁是自1918年甲型流感（H1N1）大流行以来在呼吸道病毒中所见最为严重的。在本文中，我们着重回顾了流行病学建模的结果，特别是分数阶流行病模型，并总结了不同类型的分数阶流行病模型，包括分数阶易感-感染-康复（SIR）模型、易感-暴露-感染-康复（SEIR）模型、易感-暴露-感染-无症状-康复（SEIAR）模型等。此外，我们针对单阶和多阶分数阶微分方程的情况提出了一个通用的分数阶SEIAR模型。还提出了一种基于改进的混合Nelder-Mead单纯形搜索和粒子群优化的可行且可靠的参数估计方法，以使用分数阶SEIAR模型拟合实际数据。我们介绍的求解分数阶流行病模型的有效方法构建了一种简单有效的解析技术，该技术可以轻松扩展并应用于其他分数阶模型，并且有助于指导相关机构预防或控制甚至预测传染病的爆发。
