A Model for Reinfections and the Transition of Epidemics

Reinfections of infected individuals during a viral epidemic contribute to the continuation of the infection for longer periods of time. In an epidemic, contagion starts with an infection wave, initially growing exponentially fast until it reaches a maximum number of infections, following which it wanes towards an equilibrium state of zero infections, assuming that no new variants have emerged. If reinfections are allowed, multiple such infection waves might occur, and the asymptotic equilibrium state is one in which infection rates are not negligible. This paper analyzes such situations by expanding the traditional SIR model to include two new dimensionless parameters, ε and θ, characterizing, respectively, the kinetics of reinfection and a delay time, after which reinfection commences. We find that depending on these parameter values, three different asymptotic regimes develop. For relatively small θ, two of the regimes are asymptotically stable steady states, approached either monotonically, at larger ε (corresponding to a stable node), or as waves of exponentially decaying amplitude and constant frequency, at smaller ε (corresponding to a spiral). For θ values larger than a critical, the asymptotic state is a periodic pattern of constant frequency. However, when ε is sufficiently small, the asymptotic state is a wave. We delineate these regimes and analyze the dependence of the corresponding population fractions (susceptible, infected and recovered) on the two parameters ε and θ and on the reproduction number R₀. The results provide insights into the evolution of contagion when reinfection and the waning of immunity are taken into consideration. A related byproduct is the finding that the conventional SIR model is singular at large times, hence the specific quantitative estimate for herd immunity it predicts will likely not materialize.

Equilibrium States in Open Quantum Systems

The aim of this paper is to study the question of whether or not equilibrium states exist in open quantum systems that are embedded in at least two environments and are described by a non-Hermitian Hamilton operator H. The eigenfunctions of H contain the influence of exceptional points (EPs) and external mixing (EM) of the states via the environment. As a result, equilibrium states exist (far from EPs). They are different from those of the corresponding closed system. Their wavefunctions are orthogonal even though the Hamiltonian is non-Hermitian.

A Locomotion Control Platform With Dynamic Electromagnetic Field for Active Capsule Endoscopy

Conventional radiological and endoscopic techniques utilizing long tubes were ineffective in visualizing the small bowel mucosa until the development of wireless capsule endoscopy (WCE). WCE is a revolutionary endoscopic technology that can diagnose the complete gastrointestinal tract. However, the existing capsule technologies are passive, and thus they cannot be navigated to or held in a specific location. The design of an active capsule will present the opportunity to move and stop a device at any targeted locations leading to numerous medical applications such as drug delivery or collecting tissue samples for examinations in the laboratory. This paper implements a new locomotion methodology for WCE systems using an electromagnetic platform. The platform produces a dynamic electromagnetic field to control the motion of the capsule. The strength and the direction of the electromagnetic field that is generated by the platform are continuously adjusted in order to maintain the equilibrium state during the capsule movement. We present the detailed design of the proposed platform with an experimental setup with polyvinyl chloride tubes and ex vivo to demonstrate the performance of the capsule motion.