Abstract
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.
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