保加利亚COVID-19变速箱动力学时变逆SEIR模型的数学和计算机模拟
Mathematical and Computer Modeling of COVID-19 Transmission Dynamics in Bulgaria by Time-depended Inverse SEIR Model
摘要：
在本文中，我们探讨了一个时间依赖的SEIR模型，在该模型中，从一个选定的目标群体（人口），根据感染划分的四组感染的动力学，由一个非线性常微分方程系统建模。模型中包含了几个基本参数：感染率系数、潜伏率系数、恢复率系数。这些系数适用于每个国家的每一种具体感染，并取决于各国限制感染传播的措施和治疗感染者的方法的有效性。如果这些系数是已知的，那么求解非线性系统就有可能能够对流行病的发展做出一些假设。这就是使用保加利亚COVID-19数据首先解决所谓的“逆问题”并找到当前情况的参数的原因。反向逻辑最初用于确定模型的参数作为时间的函数，然后通过计算机解决问题。也就是说，这意味着预测这些参数的未来行为，并找到（并因此应用大规模测量，例如，隔离、消毒、限制公共活动），这是未来四个研究群体数量比例变化的合适情景。事实上，基于这些结果，我们对保加利亚的COVID-19传播动态进行了建模，并对每天的新病例数、活跃病例数和康复者人数进行了为期两周的预测。如我们所示，这种模型在保加利亚的情况下成功地进行了预测分析。我们还提供了多个数值实验的例子与可视化的结果。
英文摘要：
In this paper we explore a time-depended SEIR model, in which the dynamics of the infection in four groups from a selected target group (population), divided according to the infection, are modeled by a system of nonlinear ordinary differential equations. Several basic parameters are involved in the model: coefficients of infection rate, incubation rate, recovery rate. The coefficients are adaptable to each specific infection, for each individual country, and depend on the measures to limit the spread of the infection and the effectiveness of the methods of treatment of the infected people in the respective country. If such coefficients are known, solving the nonlinear system is possible to be able to make some hypotheses for the development of the epidemic. This is the reason for using Bulgarian COVID-19 data to first of all, solve the so-called "inverse problem" and to find the parameters of the current situation. Reverse logic is initially used to determine the parameters of the model as a function of time, followed by computer solution of the problem. Namely, this means predicting the future behavior of these parameters, and finding (and as a consequence applying mass-scale measures, e.g., distancing, disinfection, limitation of public events), a suitable scenario for the change in the proportion of the numbers of the four studied groups in the future. In fact, based on these results we model the COVID-19 transmission dynamics in Bulgaria and make a two-week forecast for the numbers of new cases per day, active cases and recovered individuals. Such model, as we show, has been successful for prediction analysis in the Bulgarian situation. We also provide multiple examples of numerical experiments with visualization of the results.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
