Fluctuations and oscillations in a simple epidemic model

We show that the simplest stochastic epidemiological models with spatial correlations exhibit two types of oscillatory behaviour in the endemic phase. In a large parameter range, the oscillations are due to resonant amplification of stochastic fluctuations, a general mechanism first reported for predator-prey dynamics. In a narrow range of parameters that includes many infectious diseases which confer long lasting immunity the oscillations persist for infinite populations. This effect is apparent in simulations of the stochastic process in systems of variable size, and can be understood from the phase diagram of the deterministic pair approximation equations. The two mechanisms combined play a central role in explaining the ubiquity of oscillatory behaviour in real data and in simulation results of epidemic and other related models.Comment: acknowledgments added; a typo in the discussion that follows Eq. (3) is corrected

Phase lag in epidemics on a network of cities

We study the synchronisation and phase-lag of fluctuations in the number of infected individuals in a network of cities between which individuals commute. The frequency and amplitude of these oscillations is known to be very well captured by the van Kampen system-size expansion, and we use this approximation to compute the complex coherence function that describes their correlation. We find that, if the infection rate differs from city to city and the coupling between them is not too strong, these oscillations are synchronised with a well defined phase lag between cities. The analytic description of the effect is shown to be in good agreement with the results of stochastic simulations for realistic population sizes.Comment: 10 pages, 6 figure

Deviant behavior of youth in the context of psychology and pedagogy

The article notes that Analysis of psychological and pedagogical literature allowed us to identify the following factors influencing formation and development of various deviant behavior forms: socio-economic, sociocultural, biological, psychological, pedagogical, subcultural. Most researchers consider the violation of social norms and norms of behavior as the main criterion for deviations and consider this phenomenon in term of “adaptation (socialization) - disadaptation (de-socialization)

Cluster approximations for infection dynamics on random networks

In this paper, we consider a simple stochastic epidemic model on large regular random graphs and the stochastic process that corresponds to this dynamics in the standard pair approximation. Using the fact that the nodes of a pair are unlikely to share neighbors, we derive the master equation for this process and obtain from the system size expansion the power spectrum of the fluctuations in the quasi-stationary state. We show that whenever the pair approximation deterministic equations give an accurate description of the behavior of the system in the thermodynamic limit, the power spectrum of the fluctuations measured in long simulations is well approximated by the analytical power spectrum. If this assumption breaks down, then the cluster approximation must be carried out beyond the level of pairs. We construct an uncorrelated triplet approximation that captures the behavior of the system in a region of parameter space where the pair approximation fails to give a good quantitative or even qualitative agreement. For these parameter values, the power spectrum of the fluctuations in finite systems can be computed analytically from the master equation of the corresponding stochastic process.Comment: the notation has been changed; Ref. [26] and a new paragraph in Section IV have been adde

Epidemiological impact of waning immunization on a vaccinated population

This is an epidemiological SIRV model based study that is de- signed to analyze the impact of vaccination in containing infection spread, in a 4-tiered population compartment comprised of susceptible, infected, recov- ered and vaccinated agents. While many models assume a lifelong protection through vaccination, we focus on the impact of waning immunization due to conversion of vaccinated and recovered agents back to susceptible ones. Two asymptotic states exist, the \disease-free equilibrium" and the \endemic equi- librium" and we express the transitions between these states as function of the vaccination and conversion rates and using the basic reproduction number. We nd that the vaccination of newborns and adults have dierent consequences on controlling an epidemic. Also, a decaying disease protection within the re- covered sub-population is not sucient to trigger an epidemic on the linear level. We perform simulations for a parameter set modelling a disease with waning immunization like pertussis. For a diusively coupled population, a transition to the endemic state can proceed via the propagation of a traveling infection wave, described successfully within a Fisher-Kolmogorov framework

СИНХРОННАЯ ЭЛЕКТРОЭНЦЕФАЛОГРАФИЯ И ФУНКЦИОНАЛЬНАЯ МАГНИТНО-РЕЗОНАНСНАЯ ТОМОГРАФИЯ В ПРЕДОПЕРАЦИОННОЙ ПОДГОТОВКЕ ПАЦИЕНТОВ С ФАРМАКОРЕЗИСТЕНТНОЙ ЭПИЛЕПСИЕЙ. МЕТОДОЛОГИЯ И ОПЫТ КЛИНИЧЕСКОГО ПРИМЕНЕНИЯ

Approximately 30% of patients with symptomatic epilepsy have pharmacoresistant seizures refractory to medical therapy. The most effective treatment modality is microsurgical resection of whole epileptogenic zone, not only visible on MRI lesion. However, in some cases patients still have seizures after operation. We provide a method of simultaneous EEG-fMRI to more accurate localization of epileptogenic zone after failed surgery. Here we present our experience of gamma knife stereotactic radiosurgery for patient harboring mesial temporal lobe epilepsy using EEG-fMRI for confirmation of residual epileptogenic zone.Около 30% пациентов с  симптоматической эпилепсией проявляют фармакорезистентность  — неэффективность многокомпонентного медикаментозного лечения. Наиболее эффективным методом радикального лечения симптоматической эпилепсии является микрохирургическое удаление не только видимого при магнитно-резонансной томографии патологического очага, но и всей эпилептогенной зоны. Тем не менее в некоторых случаях возникает рецидив заболевания. Для более точного определения эпилептогенной зоны в послеоперационном периоде мы предлагаем использовать метод синхронной электроэнцефалографии и функциональной магнитнорезонансной томографии и  описываем особенности его рутинного применения. Клиническое наблюдение демонстрирует возможность успешного радиохирургического лечения на  аппарате Leksell Gamma Knife Perfexion пациента с  рецидивом мезиальной височной эпилепсии после хирургического лечения, для чего использовали данные о локализации эпилептогенного очага, полученные с помощью описанного метода

A Simple Stochastic Model with Environmental Transmission Explains Multi-Year Periodicity in Outbreaks of Avian Flu

Avian influenza virus reveals persistent and recurrent outbreaks in North American wild waterfowl, and exhibits major outbreaks at 2–8 years intervals in duck populations. The standard susceptible-infected- recovered (SIR) framework, which includes seasonal migration and reproduction, but lacks environmental transmission, is unable to reproduce the multi-periodic patterns of avian influenza epidemics. In this paper, we argue that a fully stochastic theory based on environmental transmission provides a simple, plausible explanation for the phenomenon of multi-year periodic outbreaks of avian flu. Our theory predicts complex fluctuations with a dominant period of 2 to 8 years which essentially depends on the intensity of environmental transmission. A wavelet analysis of the observed data supports this prediction. Furthermore, using master equations and van Kampen system-size expansion techniques, we provide an analytical expression for the spectrum of stochastic fluctuations, revealing how the outbreak period varies with the environmental transmission

Comparative Analysis of the QbD Approach in the Pharmaceutical Industry

Introduction. In the development and introduction of medicines into production, the aim of pharmaceutical manufacturers is to comply with the principle of «Quality-by-Design» (QbD). The International Council for Harmonisation (ICH) has created a number of GxP standards, which have become the regulatory framework for the development of documentation regulating the requirements for the development and production of drug products for countries focused on bringing their products to the world pharmaceutical market. The analysis of the system of regulation of pharmaceutical stages of development of new drugs in the territory of the Eurasian Economic Union was not considered, but for the formation of a systematic approach to the management of the process of pharmaceutical development it is necessary to describe them.Aim. To analyze the possibility of applying the QbD principle to the process of drug development at domestic pharmaceutical enterprises.Materials and methods. Content analysis of scientific publications, system and comparative analysis, sociological methods of research in the field of pharmaceutical development.Results and discussions. Regulatory state requirements to the organization and conduct of drug development procedures are analyzed and described. A number of systemic and sectoral problems typical for domestic pharmaceutical manufacturers in the organization of the development and implementation of new drug products. It is established that one of the main problems for Russian enterprises was the organization of the process as a whole and its individual procedures. To solve the problem of organization of procedures for the development and implementation of new medicines, we formed a methodological support, developed on the basis of a systematic approach and international requirements from the quality system.Conclusion. The main problem identified by the manufacturers is the lack of methodological support for the organization of the processes of pharmaceutical development and the introduction of new drugs in the part of research going to the stage of preclinical and clinical development. The decisions adopted by the Eurasian Economic Union do not affect such aspects of pharmaceutical development regulation as the organization of processes, their management and methodological support aimed at the implementation of the QbD principle. To solve this problem, we have developed guidelines for the implementation of the processes of pharmaceutical development and the introduction of new drug products, which allowed us to apply unified and formalized approaches to their organization

Deviant behavior of youth in the context of psychology and pedagogy

The article notes that Analysis of psychological and pedagogical literature allowed us to identify the following factors influencing formation and development of various deviant behavior forms: socio-economic, sociocultural, biological, psychological, pedagogical, subcultural. Most researchers consider the violation of social norms and norms of behavior as the main criterion for deviations and consider this phenomenon in term of “adaptation (socialization) - disadaptation (de-socialization)