Modeling and Controlling the Spread of Epidemic with Various Social and Economic Scenarios

We propose a dynamical model for describing the spread of epidemics. This model is an extension of the SIQR (susceptible-infected-quarantined-recovered) and SIRP (susceptible-infected-recovered-pathogen) models used earlier to describe various scenarios of epidemic spreading. As compared to the basic SIR model, our model takes into account two possible routes of contagion transmission: direct from the infected compartment to the susceptible compartment and indirect via some intermediate medium or fomites. Transmission rates are estimated in terms of average distances between the individuals in selected social environments and characteristic time spans for which the individuals stay in each of these environments. We also introduce a collective economic resource associated with the average amount of money or income per individual to describe the socioeconomic interplay between the spreading process and the resource available to infected individuals. The epidemic-resource coupling is supposed to be of activation type, with the recovery rate governed by the Arrhenius-like law. Our model brings an advantage of building various control strategies to mitigate the effect of epidemic and can be applied, in particular, to modeling the spread of COVID-19.Comment: 14 pages, 6 figures, 5 table

Effects of interatomic interaction on cooperative relaxation of two-level atoms

We study effects of direct interatomic interaction on cooperative processes in atom-photon dynamics. Using a model of two-level atoms with Ising-type interaction as an example, it is demonstrated that interparticle interaction combined with atom-field coupling can introduce additional interatomic correlations acting as a phase synchronizing factor. For the case of weakly interacting atoms with $J<\hbar\omega_0$, where $J$ is the interparticle coupling constant and $\omega_0$ is the atomic frequency, dynamical regimes of cooperative relaxation of atoms are analyzed in Born-Markov approximation both numerically and using the mean field approximation. We show that interparticle correlations induced by the direct interaction result in inhibition of incoherent spontaneous decay leading to the regime of collective pulse relaxation which differs from superradiance in nature. For superradiant transition, the synchronizing effect of interatomic interaction is found to manifest itself in enhancement of superradiance. When the interaction is strong and $J>\hbar\omega_0$, one-partice one-photon transitions are excluded and transition to the regime of multiphoton relaxation occurs. Using a simple model of two atoms in a high-Q single mode cavity we show that such transition is accompanied by Rabi oscillations involving many-atom multiphoton states. Dephasing effect of dipole-dipole interaction and solitonic mechanism of relaxation are discussed.Comment: 34 pages, 8 figure

РАЗРАБОТКА И ЭКСПЕРИМЕНТАЛЬНЫЕ ИССЛЕДОВАНИЯ НЕЙРОПОРТА ДЛЯ ТЕРАПИИ ГЛИОМЫ ГОЛОВНОГО МОЗГА

Current paper presents the results of the system development for intracranial implantation aimed on therapy and prevention of brain gliomas relapse. The main property of the system, in prospective,  will be to direct the growth of glioma cells localized in the region  adjacent to the site of the removed tumor along the fi bers towards  the proximal part of the fiber-optic scaffold (neuroport). Such  approach will allow carrying out cells diagnostics by the  photoluminescence signal and provide subsequent destruction of  malignant cells by photodynamic action. Besides, this system could  be used for monitoring the processes occurring in the probed area in order to control the possible relapses. The localization of cells along  the fi ber structures covered with gelatin compound, which is the  source of amino acids during cultivation, was shown during the glioma cells growth dynamics study. Moreover, four different designs of intracranial scaffold models, serving as ports for diagnostic and therapeutic laser radiation delivery, were developed and  successfully tested in the framework of the research. The results  obtained on the rats brain with induced tumors (glioma C6) after  neuroport implantation demonstrate sufficiently intense fluorescence in the tumor bed after intravenous injection of the  nonmetallic sulfonated phthalocyanine based photosensitizer, and a  pronounced photodynamic effect leading to total destruction of the  tumor. In this way, the results of this study open the prospects of creating the neuroport with an internal fi ber structure that focuses the glioma cells growth.В работе представлены результаты разработки системы для внутричерепной имплантации с целью терапии и предотвращения рецидивирования глиом головного. Основное свойство  системы в перспективе будет состоять в том, чтобы направить рост клеток глиомы,  локализованных в области, прилегающей к месту удаленной опухоли, вдоль волокон по  направлению к проксимальной части волоконно-оптического имплантата (нейропорт) с  целью их регистрации по сигналу фотолюминесценции и последующей их деструкции в  результате фотодинамического воздействия. Такое устройство должно обеспечить  мониторинг процессов, происходящих в зондируемой области с целью контроля процессов  рецидивирования. В ходе данного исследования динамики роста клеток глиомы показана  локализация клеток вдоль волоконных структур, покрытых желатином, который является  источником аминокислот при культивировании. Также в ходе работы были разработаны и  успешно апробированы четыре различных конструкции макетов внутричерепных  имплантатов, выполняющие роль портов для доставки диагностического и терапевтического лазерного излучения. Получены на головном мозге крыс с индуцированными опухолями  (глиома С6) после имплантации нейропорта, демонстрирующие достаточно интенсивную  флуоресценцию в ложе опухоли при внутривенном введении фотосенсибилизатора на  основе безметального сульфированного фталоцианина и выраженный фотодинамический  эффект, приведший к тотальному разрушению опухоли. Полученные результаты открывают  перспективы создания нейропорта с внутренней волоконной структурой, фокусирующей рост клеток глиомы

A toy model for the epidemic-driven collapse in a system with limited economic resource

Based on a toy model for a trivial socioeconomic system, we demonstrate that the activation-type mechanism of the epidemic-resource coupling can lead to the collapsing effect opposite to thermal explosion. We exploit a SIS-like (susceptible-infected-susceptible) model coupled with the dynamics of average economic resource for a group of active economic agents. The recovery rate of infected individuals is supposed to obey the Arrhenius-like law, resulting in a mutual negative feedback between the number of active agents and resource acquisition. The economic resource is associated with the average amount of money or income per agent and formally corresponds to the effective market temperature of agents, with their income distribution obeying the Boltzmann–Gibbs statistics. A characteristic level of resource consumption is associated with activation energy. We show that the phase portrait of the system features a collapse phase, in addition to the well-known disease-free and endemic phases. The epidemic intensified by the increasing resource deficit can ultimately drive the system to a collapse at nonzero activation energy because of limited resource. We briefly discuss several collapse mitigation strategies involving either financial instruments like subsidies or social regulations like quarantine

Analysis of forming flexible production with the use of simulation models

Исследуются участки штамповки деталей из штучных заготовок и полосы. Составлены сети Петри, с их помощью выявлены узкие места в работе участков. Предлагаются усовершенствованные алгоритмы организации производства. Приводятся результаты компьютерного моделирования исследуемых технологических процессов. Сформулирована методика анализа гибкого штамповочного производства и даны рекомендации по повышению его эффективности.The paper focuses on investigation of automatic press forming sections from piece slugs and strips. With the help of Petri nets Bottlenecks in work of sections are revealed. As a result advanced algorithms of the manufacture organization are offered. Also results of computer modeling of investigated technological processes are supplied. The technique of the adjustable forming manufactures analysis is formulated and recommendations about increase of its efficiency are made