Dos Reis Eduardo V M, Savi Marcelo A
Department of Mechanical Engineering, Center for Nonlinear Mechanics, Universidade Federal do Rio de Janeiro, COPPE, P.O. Box 68 503, Rio de Janeiro, RJ Brazil.
Eur Phys J Spec Top. 2022;231(5):893-904. doi: 10.1140/epjs/s11734-021-00340-5. Epub 2021 Nov 25.
Nonlinear dynamics perspective is an interesting approach to describe COVID-19 epidemics, providing information to support strategic decisions. This paper proposes a dynamical map to describe COVID-19 epidemics based on the classical susceptible-exposed-infected-recovered (SEIR) differential model, incorporating vaccinated population. On this basis, the novel map represents COVID-19 discrete-time dynamics by adopting three populations: infected, cumulative infected and vaccinated. The map promotes a dynamical description based on algebraic equations with a reduced number of variables and, due to its simplicity, it is easier to perform parameter adjustments. In addition, the map description allows analytical calculations of useful information to evaluate the epidemic scenario, being important to support strategic decisions. In this regard, it should be pointed out the estimation of the number deaths, infection rate and the herd immunization point. Numerical simulations show the model capability to describe COVID-19 dynamics, capturing the main features of the epidemic evolution. Reported data from Germany, Italy and Brazil are of concern showing the map ability to describe different scenario patterns that include multi-wave pattern with bell shape and plateaus characteristics. The effect of vaccination is analyzed considering different campaign strategies, showing its importance to control the epidemics.
非线性动力学视角是描述新冠疫情的一种有趣方法，可为战略决策提供支持信息。本文基于经典的易感-暴露-感染-康复（SEIR）微分模型，纳入接种疫苗人群，提出了一种描述新冠疫情的动态映射。在此基础上，该新型映射通过采用感染人群、累计感染人群和接种疫苗人群这三类人群来表示新冠疫情的离散时间动态。该映射促进了基于变量数量减少的代数方程的动态描述，并且由于其简单性，更容易进行参数调整。此外，该映射描述允许对评估疫情形势的有用信息进行解析计算，这对于支持战略决策很重要。在这方面，应指出死亡人数、感染率和群体免疫点的估计。数值模拟显示了该模型描述新冠疫情动态的能力，捕捉到了疫情演变的主要特征。来自德国、意大利和巴西的报告数据令人关注，显示了该映射描述不同情景模式的能力，这些模式包括具有钟形和平原特征的多波模式。考虑不同的疫苗接种策略分析了疫苗接种的效果，显示了其对控制疫情的重要性。
