Atangana Abdon, İğret Araz Seda
Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, South Africa.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan.
Results Phys. 2021 Oct;29:104694. doi: 10.1016/j.rinp.2021.104694. Epub 2021 Aug 18.
Several collected data representing the spread of some infectious diseases have demonstrated that the spread does not really exhibit homogeneous spread. Clear examples can include the spread of Spanish flu and Covid-19. Collected data depicting numbers of daily new infections in the case of Covid-19 from countries like Turkey, Spain show three waves with different spread patterns, a clear indication of crossover behaviors. While modelers have suggested many mathematical models to depicting these behaviors, it becomes clear that their mathematical models cannot really capture the crossover behaviors, especially passage from deterministic resetting to stochastics. Very recently Atangana and Seda have suggested a concept of piecewise modeling consisting in defining a differential operator piece-wisely. The idea was first applied in chaos and outstanding patterns were captured. In this paper, we extend this concept to the field of epidemiology with the aim to depict waves with different patterns. Due to the novelty of this concept, a different approach to insure the existence and uniqueness of system solutions are presented. A piecewise numerical approach is presented to derive numerical solutions of such models. An illustrative example is presented and compared with collected data from 3 different countries including Turkey, Spain and Czechia. The obtained results let no doubt for us to conclude that this concept is a new window that will help mankind to better understand nature.
一些收集到的代表某些传染病传播情况的数据表明，这种传播并非真正呈现均匀扩散。明显的例子包括西班牙流感和新冠疫情的传播。收集到的描绘土耳其、西班牙等国新冠疫情每日新增感染病例数的数据显示出具有不同传播模式的三波疫情，这清楚地表明了交叉行为。虽然建模者提出了许多数学模型来描述这些行为，但很明显，他们的数学模型无法真正捕捉到交叉行为，尤其是从确定性重置到随机性的转变。最近，阿坦加纳和塞达提出了一种分段建模的概念，即逐段定义一个微分算子。这个想法最初应用于混沌领域，并捕捉到了显著的模式。在本文中，我们将这个概念扩展到流行病学领域，旨在描绘不同模式的疫情波。由于这个概念的新颖性，我们提出了一种不同的方法来确保系统解的存在性和唯一性。我们提出了一种分段数值方法来推导此类模型的数值解。给出了一个示例，并与包括土耳其、西班牙和捷克在内的3个不同国家收集的数据进行了比较。所得结果让我们毫无疑问地得出结论，这个概念是一扇新窗口，将有助于人类更好地理解自然。
