流行病学中的确定性模型：从建模到实现
Deterministic Models in Epidemiology: From Modeling to Implementation
摘要：
生物疾病的突然爆发和传播一直是人类长期关注的问题。长期以来，数学建模一直是研究、预测和控制传染病在个体间传播的一种简单而有效的工具。文献中报道了大量关于流行病模型及其变体的工作。为了更好地预测特定疾病的动态，重要的是采用最合适的模型。在本文中，我们研究了一些广受赞赏的确定性流行病模型，其中人口被划分为基于每个人的健康状况的隔间。特别是，我们提供了这样的模型的人口分类，并研究他们每个人的数学公式，近平衡点的稳定性，疾病爆发的阈值条件（基本繁殖比）。此外，我们讨论了各种影响因素，需要考虑在流行病建模。本文的主要目的是提供一个基本的理解的数学复杂性所产生的确定性流行病模型的帮助下，通过实施获得的图形说明。
英文摘要：
The abrupt outbreak and transmission of biological diseases has always been a long-time concern of humankind. For long, mathematical modeling has served as a simple and yet efficient tool to investigate, predict, and control spread of communicable diseases through individuals. A myriad of works on epidemic models and their variants have been reported in the literature. For better prediction of the dynamics of a particular disease, it is important to adopt the most suitable model. In this paper, we study some of the widely-appreciated deterministic epidemic models in which the population is divided into compartments based on the health status of each individual. In particular, we provide a demographic classification of such models and study each of them in terms of mathematical formulation, near equilibrium point stability properties, and disease outbreak threshold conditions (basic reproduction ratio). Furthermore, we discuss the various influential factors that need to be considered during epidemic modeling. The main objective of this article is to provide a basic understanding of the mathematical complexity incurred in deterministic epidemic models with the aid of graphical illustrations obtained through implementation.
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