Parametric inference for discretely observed multidimensional diffusions with small diffusion coefficient

We consider a multidimensional diffusion X with drift coefficient b({\alpha},X(t)) and diffusion coefficient {\epsilon}{\sigma}({\beta},X(t)). The diffusion is discretely observed at times t_k=k{\Delta} for k=1..n on a fixed interval [0,T]. We study minimum contrast estimators derived from the Gaussian process approximating X for small {\epsilon}. We obtain consistent and asymptotically normal estimators of {\alpha} for fixed {\Delta} and {\epsilon}\rightarrow0 and of ({\alpha},{\beta}) for {\Delta}\rightarrow0 and {\epsilon}\rightarrow0. We compare the estimators obtained with various methods and for various magnitudes of {\Delta} and {\epsilon} based on simulation studies. Finally, we investigate the interest of using such methods in an epidemiological framework.Comment: 31 pages, 2 figures, 2 table

Approximation of epidemic models by diffusion processes and their statistical inference

Multidimensional continuous-time Markov jump processes $(Z(t))$ on $\mathbb{Z}^p$ form a usual set-up for modeling $SIR$-like epidemics. However, when facing incomplete epidemic data, inference based on $(Z(t))$ is not easy to be achieved. Here, we start building a new framework for the estimation of key parameters of epidemic models based on statistics of diffusion processes approximating $(Z(t))$. First, \previous results on the approximation of density-dependent $SIR$-like models by diffusion processes with small diffusion coefficient $\frac{1}{\sqrt{N}}$, where $N$ is the population size, are generalized to non-autonomous systems. Second, our previous inference results on discretely observed diffusion processes with small diffusion coefficient are extended to time-dependent diffusions. Consistent and asymptotically Gaussian estimates are obtained for a fixed number $n$ of observations, which corresponds to the epidemic context, and for $N\rightarrow \infty$. A correction term, which yields better estimates non asymptotically, is also included. Finally, performances and robustness of our estimators with respect to various parameters such as $R_0$ (the basic reproduction number), $N$, $n$ are investigated on simulations. Two models, $SIR$ and $SIRS$, corresponding to single and recurrent outbreaks, respectively, are used to simulate data. The findings indicate that our estimators have good asymptotic properties and behave noticeably well for realistic numbers of observations and population sizes. This study lays the foundations of a generic inference method currently under extension to incompletely observed epidemic data. Indeed, contrary to the majority of current inference techniques for partially observed processes, which necessitates computer intensive simulations, our method being mostly an analytical approach requires only the classical optimization steps.Comment: 30 pages, 10 figure

Impact of the Infection Period Distribution on the Epidemic Spread in a Metapopulation Model

Epidemic models usually rely on the assumption of exponentially distributed sojourn times in infectious states. This is sometimes an acceptable approximation, but it is generally not realistic and it may influence the epidemic dynamics as it has already been shown in one population. Here, we explore the consequences of choosing constant or gamma-distributed infectious periods in a metapopulation context. For two coupled populations, we show that the probability of generating no secondary infections is the largest for most parameter values if the infectious period follows an exponential distribution, and we identify special cases where, inversely, the infection is more prone to extinction in early phases for constant infection durations. The impact of the infection duration distribution on the epidemic dynamics of many connected populations is studied by simulation and sensitivity analysis, taking into account the potential interactions with other factors. The analysis based on the average nonextinct epidemic trajectories shows that their sensitivity to the assumption on the infectious period distribution mostly depends on , the mean infection duration and the network structure. This study shows that the effect of assuming exponential distribution for infection periods instead of more realistic distributions varies with respect to the output of interest and to other factors. Ultimately it highlights the risk of misleading recommendations based on modelling results when models including exponential infection durations are used for practical purposes

Основні риси сучасної правової системи України

Правова система, що досліджується в науковій статті, має суттєве значення в процесі створення та функціонування правових інститутів. Проаналізована категорія має важливе значення, оскільки сприяє реалізації визнаних державою завдань та перспектив. Тому, цілком правомірним є дослідження значення правової системи для формування та розвитку громадського суспільства та правової держави. Ключові слова: правова система, правовий інститут, громадянське суспільство, правова держава.В статье анализируются теоретические и практические проблемы развития правовой системы Украины. Обосновывается мысль о необходимости подготовки и принятия концепции развития правового регулирования общественных отношений в Украине и законодательных актов. Проанализировано взгляды ученых относительно научных подходов к исследованию правовой системы. Анализируется соотношение и взаимодействие таких важных категорий, как правовая система и правовое государство. Ключевые слова: правовая система, правовой институт, гражданское общество, правовое государство.Theoretical and practical problems of Ukrainian legal system development are analyzed in the article. The thought about the necessity of preparation and adoption of concept of the development of social relations legal regulation in Ukraine and legislative regulations is grounded. The scientist’s views as for scientific approaches to the legal system study are analyzed. The correlation and interaction of such important categories as legal system and law-governed state are analyzed. Key words: legal system, legal institution, civil society, law-governed stare

Modelling effectiveness of herd level vaccination against Q fever in dairy cattle

Q fever is a worldwide zoonosis caused by the bacterium Coxiella burnetii. The control of this infection in cattle is crucial: infected ruminants can indeed encounter reproductive disorders and represent the most important source of human infection. In the field, vaccination is currently advised in infected herds but the comparative effectiveness of different vaccination protocols has never been explored: the duration of the vaccination programme and the category of animals to be vaccinated have to be determined. Our objective was to compare, by simulation, the effectiveness over 10 years of three different vaccination strategies in a recently infected dairy cattle herd

Medication Sales and Syndromic Surveillance, France

Real-time over-the-counter drug sales provide an additional tool for disease surveillance

Does the Effectiveness of Control Measures Depend on the Influenza Pandemic Profile?

BACKGROUND: Although strategies to contain influenza pandemics are well studied, the characterization and the implications of different geographical and temporal diffusion patterns of the pandemic have been given less attention. METHODOLOGY/MAIN FINDINGS: Using a well-documented metapopulation model incorporating air travel between 52 major world cities, we identified potential influenza pandemic diffusion profiles and examined how the impact of interventions might be affected by this heterogeneity. Clustering methods applied to a set of pandemic simulations, characterized by seven parameters related to the conditions of emergence that were varied following Latin hypercube sampling, were used to identify six pandemic profiles exhibiting different characteristics notably in terms of global burden (from 415 to >160 million of cases) and duration (from 26 to 360 days). A multivariate sensitivity analysis showed that the transmission rate and proportion of susceptibles have a strong impact on the pandemic diffusion. The correlation between interventions and pandemic outcomes were analyzed for two specific profiles: a fast, massive pandemic and a slow building, long-lasting one. In both cases, the date of introduction for five control measures (masks, isolation, prophylactic or therapeutic use of antivirals, vaccination) correlated strongly with pandemic outcomes. Conversely, the coverage and efficacy of these interventions only moderately correlated with pandemic outcomes in the case of a massive pandemic. Pre-pandemic vaccination influenced pandemic outcomes in both profiles, while travel restriction was the only measure without any measurable effect in either. CONCLUSIONS: our study highlights: (i) the great heterogeneity in possible profiles of a future influenza pandemic; (ii) the value of being well prepared in every country since a pandemic may have heavy consequences wherever and whenever it starts; (iii) the need to quickly implement control measures and even to anticipate pandemic emergence through pre-pandemic vaccination; and (iv) the value of combining all available control measures except perhaps travel restrictions

Influenza A Gradual and Epochal Evolution: Insights from Simple Models

The recurrence of influenza A epidemics has originally been explained by a “continuous antigenic drift” scenario. Recently, it has been shown that if genetic drift is gradual, the evolution of influenza A main antigen, the haemagglutinin, is punctuated. As a consequence, it has been suggested that influenza A dynamics at the population level should be approximated by a serial model. Here, simple models are used to test whether a serial model requires gradual antigenic drift within groups of strains with the same antigenic properties (antigenic clusters). We compare the effect of status based and history based frameworks and the influence of reduced susceptibility and infectivity assumptions on the transient dynamics of antigenic clusters. Our results reveal that the replacement of a resident antigenic cluster by a mutant cluster, as observed in data, is reproduced only by the status based model integrating the reduced infectivity assumption. This combination of assumptions is useful to overcome the otherwise extremely high model dimensionality of models incorporating many strains, but relies on a biological hypothesis not obviously satisfied. Our findings finally suggest the dynamical importance of gradual antigenic drift even in the presence of punctuated immune escape. A more regular renewal of susceptible pool than the one implemented in a serial model should be part of a minimal theory for influenza at the population level