论文标题
通过重新感染流行动力学的建模，分析，可观察性和可识别性
Modelling, Analysis, Observability and Identifiability of Epidemic Dynamics with Reinfections
论文作者
论文摘要
我们在本文中考虑了一般的SEIRS模型，描述了传染病的动态，包括潜伏期，免疫力减弱和感染诱导的死亡率。我们得出了一个无限的微分方程系统，该系统提供了相同感染过程的图像，但还计算了重新感染。相应的库奇问题的存在和唯一性是在合适的序列值函数的合适空间中确定的，并且根据基本繁殖数的值来表征溶液的渐近行为。这允许确定与流行平衡时与人群相关的几个平均数量。然后，我们展示如何使用感染个体的数量共同测量受感染者的数量，并为简单的SIS模型提供可观察性和可识别性，而这两种措施都不足以确保其自身相同的属性。
We consider in this paper a general SEIRS model describing the dynamics of an infectious disease including latency, waning immunity and infection-induced mortality. We derive an infinite system of differential equations that provides an image of the same infection process, but counting also the reinfections. Existence and uniqueness of the corresponding Cauchy problem is established in a suitable space of sequence valued functions, and the asymptotic behavior of the solutions is characterized, according to the value of the basic reproduction number. This allows to determine several mean numbers of reinfections related to the population at endemic equilibrium. We then show how using jointly measurement of the number of infected individuals and of the number of primo-infected provides observability and identifiability to a simple SIS model for which none of these two measures is sufficient to ensure on its own the same properties.
