A stochastic population model of cholera disease

<p style='text-indent:20px;'>A cholera population model with stochastic transmission and stochasticity on the environmental reservoir of the cholera bacteria is presented. It is shown that solutions are well-behaved. In comparison with the underlying deterministic model, the stochastic perturbation is shown to enhance stability of the disease-free equilibrium. The main extinction theorem is formulated in terms of an invariant which is a modification of the basic reproduction number of the underlying deterministic model. As an application, the model is calibrated as for a certain province of Nigeria. In particular, a recent outbreak (2019) in Nigeria is analysed and featured through simulations. Simulations include making forward projections in the form of confidence intervals. Also, the extinction theorem is illustrated through simulations.</p>

Backward waves leaving the metamaterial

The medium is composed of plane-parallel monolayers consisting of Huygens elements. In the molecular optics model, expressions are obtained for the reflected field, the field in the medium, and (in the case of a layer of finite thickness) behind the medium. An extinction theorem is considered, and an expression for the refractive index is introduced. Under certain conditions, such a medium can behave like a medium with a unit, zero, or negative real part of the refractive index at a given frequency. The condition for the realization of a magnetic mirror is formulated. In the case of a medium layer of finite thickness, the exit of backward waves outside the medium is shown.

Elements of Classical Electrodynamics

This chapter reviews some topics in classical electrodynamics that are fundamental for modern quantum optics and that appear throughout the remaining chapters, includingelectric dipole radiation, electromagnetic energy, Abraham and Minkowski momenta in dielectric media, photon momentum, and Rayleigh scattering. Other foundational topics treatedare Earnshaw’s theorem, gauges and Lorentz transformations of fields, radiation reaction, the Ewald-Oseen extinction theorem, different forms of stress tensors in dielectric media, and the optical theorem.