We investigate a new fundamental property of infectious diseases with natural adaptive immunity that weakens over time. Numerical experiments with a model of the Covid-19 epidemic in Moscow have demonstrated that when the reproduction number R0 is about 4, a qualitative change (bifurcation) occurs in the behavior of the virus-human system. Below this value, the long-term forecast tends to undamped oscillations; above it, the forecast shows damped oscillations: the amplitudes of epidemic waves decrease gradually, with a constant, very high background level of morbidity that keeps the natural immunity near 100%. To confirm this result analytically, we use an original modification of the Euler-Lotka renewal equation, which describes the dynamics of infected patients distributed by disease duration (time since infection) and accounts for immunity. To construct a bifurcation diagram, which illustrates the dependence of the equilibrium stability on the parameter R0, we linearize the equation in the vicinity of the equilibrium point and examine its numerical approximation (discrete form). This approximation can be interpreted as a Leslie model, with the matrix elements dependent on the parameter R0. By examining the roots of the corresponding Lotka polynomial, we can assess the stability of the equilibrium point. For the bifurcation diagram, we use the functions obtained from the simulation of the Covid-19 epidemic in Moscow. However, observations of the epidemic in other cities and countries support the primary finding of our study regarding the attenuation of epidemic waves.

We study the effect of oblique illumination on the functioning of a plasmonic nanoantenna for chiral light. The antenna is designed to receive a structured beam of light and produce a nanosized near-field distribution that possesses non-zero orbital angular momentum. The design consists of metal (gold) micro-rods laid on a dielectric surface and is compatible with well-developed nanofabrication techniques. Experimental arrangements often require such an antenna to operate in a tilted geometry, where input light is incident on the antenna at an oblique angle. We analyze the limitations that the angled illumination imposes and discuss approaches to mitigate these limitations. Through our numerical simulations, we find that tilt angles larger than 30 degrees require modifications to the antenna design. Our analysis guides current and future experimental configurations to pushing the limits of resolution and sensitivity.

In this work, we obtained three new phosphorescent iridium complexes (Ir1-Ir3) of general stoichiometry [Ir(N^C)2(N^N)]Cl decorated with oligo(ethylene glycol) fragments to make them water soluble and biocompatible, as well as to protect them from aggregation with biomolecules such as albumin. The major photophysical characteristics of these phosphorescent complexes are determined by the nature of two cyclometallating ligands (N^C) based on 2-pyridine-benzothiophene, since quantum chemical calculations revealed that the electronic transitions responsible for the excitation and emission are localized mainly at these fragments. However, the use of various diimine ligands (N^N) proved to affect the quantum yield of phosphorescence and allows for changing the complexes sensitivity to oxygen, due to the variations in the steric accessibility of the chromophore center for O2 molecules. It was also found that the N^N ligands made possible to tune the biocompatibility of the resulting compounds. The wavelengths of the Ir1-Ir3 emission maxima fall in the range of 630-650 nm, the quantum yields reach 17% (Ir1) in deaerated solution and sensitivity to molecular oxygen, estimated as ratio of emission lifetime in deaerated and aerated water solution, displays the highest value 8.2 for Ir1. The obtained complexes feature low toxicity, good water solubility and the absence of a significant effect of biological environment components on the parameters of their emission. Of the studied compounds Ir1 and Ir2 have been chosen for in vitro and in vivo biological experiments aimed at estimation of oxygen concentration in cell lines and tumors. These sensors have demonstrated their effectiveness for mapping the distribution of oxygen and for monitoring hypoxia in biological objects studied.