This paper is concerned with the observer design problem for a system composed of two Kermack–McKendrick equations considering reinfection. The system is described by two first-order hyperbolic equations that have a time lag in the nonlocal boundary condition. The element of time lag can be expressed by a transport equation. As a result, the system with one delay is equivalently written by a 3 × 3 hyperbolic equations system. In this paper, we construct observers using a backstepping methodology of PDEs. Especially, decoupling transformations are used. Numerical experimental results are also given.

中文翻译：

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考虑再感染的传染病 PDE 模型的观察者设计

本文关注由两个考虑再感染的 Kermack-McKendrick 方程组成的系统的观测器设计问题。该系统由两个在非局部边界条件下具有时滞的一阶双曲方程描述。时间滞后的元素可以用传输方程表示。因此，具有一个延迟的系统等效地写成一个3×3双曲方程组。在本文中，我们使用偏微分方程的反推方法构建观察者。特别是，使用解耦变换。还给出了数值实验结果。