Gumel Abba B, Iboi Enahoro A, Ngonghala Calistus N, Elbasha Elamin H
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, 85287, USA.
Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, 0002, South Africa.
Infect Dis Model. 2020 Nov 30;6:148-168. doi: 10.1016/j.idm.2020.11.005. eCollection 2021.
The novel coronavirus (COVID-19) pandemic that emerged from Wuhan city in December 2019 overwhelmed health systems and paralyzed economies around the world. It became the most important public health challenge facing mankind since the 1918 Spanish flu pandemic. Various theoretical and empirical approaches have been designed and used to gain insight into the transmission dynamics and control of the pandemic. This study presents a primer for formulating, analysing and simulating mathematical models for understanding the dynamics of COVID-19. Specifically, we introduce simple compartmental, Kermack-McKendrick-type epidemic models with homogeneously- and heterogeneously-mixed populations, an endemic model for assessing the potential population-level impact of a hypothetical COVID-19 vaccine. We illustrate how some basic non-pharmaceutical interventions against COVID-19 can be incorporated into the epidemic model. A brief overview of other kinds of models that have been used to study the dynamics of COVID-19, such as agent-based, network and statistical models, is also presented. Possible extensions of the basic model, as well as open challenges associated with the formulation and theoretical analysis of models for COVID-19 dynamics, are suggested.
2019年12月在武汉市出现的新型冠状病毒（COVID-19）大流行使全球卫生系统不堪重负，经济陷入瘫痪。它成为自1918年西班牙流感大流行以来人类面临的最重要的公共卫生挑战。人们设计并采用了各种理论和实证方法来深入了解该大流行的传播动态和防控措施。本研究提供了一个入门指南，用于构建、分析和模拟数学模型，以理解COVID-19的动态变化。具体而言，我们介绍了简单的 compartments 模型、具有均匀混合和非均匀混合人群的Kermack-McKendrick型流行病模型，以及一个用于评估假设的COVID-19疫苗对潜在人群水平影响的地方病模型。我们说明了如何将一些针对COVID-19的基本非药物干预措施纳入流行病模型。还简要概述了用于研究COVID-19动态变化的其他类型的模型，如基于主体的模型、网络模型和统计模型。文中还提出了基本模型可能的扩展方向，以及与COVID-19动态模型的构建和理论分析相关的开放性挑战。
