Chair of Applied Mathematics and Numerical Analysis, School of Mathematics and Natural Sciences, University of Wuppertal, Wuppertal 42119, Germany.
Chair of Health Economics, Faculty of Management and Economics, University of Wuppertal, Wuppertal 42119, Germany.
Math Biosci Eng. 2022 Jan;19(2):1213-1238. doi: 10.3934/mbe.2022056. Epub 2021 Dec 1.
In the context of 2019 coronavirus disease (COVID-19), considerable attention has been paid to mathematical models for predicting country- or region-specific future pandemic developments. In this work, we developed an SVICDR model that includes a susceptible, an all-or-nothing vaccinated, an infected, an intensive care, a deceased, and a recovered compartment. It is based on the susceptible-infectious-recovered (SIR) model of Kermack and McKendrick, which is based on ordinary differential equations (ODEs). The main objective is to show the impact of parameter boundary modifications on the predicted incidence rate, taking into account recent data on Germany in the pandemic, an exponential increasing vaccination rate in the considered time window and trigonometric contact and quarantine rate functions. For the numerical solution of the ODE systems a model-specific non-standard finite difference (NSFD) scheme is designed, that preserves the positivity of solutions and yields the correct asymptotic behaviour.
在 2019 冠状病毒病（COVID-19）的背景下，人们对预测特定国家或地区未来大流行发展的数学模型给予了极大关注。在这项工作中，我们开发了一个 SVICDR 模型，其中包含易感者、全部或无疫苗接种者、感染者、重症监护者、死亡者和康复者。它基于 Kermack 和 McKendrick 的易感-感染-康复（SIR）模型，该模型基于常微分方程（ODE）。主要目的是展示参数边界修改对预测发病率的影响，同时考虑到大流行期间德国的最新数据、考虑时间窗内指数增加的疫苗接种率以及三角函数接触和隔离率函数。为了对 ODE 系统进行数值求解，设计了一种特定于模型的非标准有限差分（NSFD）方案，该方案保留了解的正定性，并产生了正确的渐近行为。
