Combining social and genetic networks to study HIV transmission in mixing risk groups

Reconstruction of HIV transmission networks is important for understanding and preventing the spread of the virus and drug resistant variants. Mixing risk groups is important in network analysis of HIV in order to assess the role of transmission between risk groups in the HIV epidemic. Most of the research focuses on the transmission within HIV risk groups, while transmission between different risk groups has been less studied. We use a proposed filter-reduction method to infer hypothetical transmission networks of HIV by combining data from social and genetic scales. We modified the filtering process in order to include mixing risk groups in the model. For this, we use the information on phylogenetic clusters obtained through phylogenetic analysis. A probability matrix is also defined to specify contact rates between individuals form the same and different risk groups. The method converts the data form each scale into network forms and combines them by overlaying and computing their intersection. We apply this method to reconstruct networks of HIV infected patients in central Italy, including mixing between risk groups. Our results suggests that bisexual behavior among Italian MSM and IDU partnership are relatively important in heterosexual transmission of HIV in central Italy.     

MCMCINLA Estimation of Missing Data and Its Application to Public Health Development in China in the Post-Epidemic Era

Medical data are often missing during epidemiological surveys and clinical trials. In this paper, we propose the MCMCINLA estimation method to account for missing data. We introduce a new latent class into the spatial lag model (SLM) and use a conditional autoregressive specification (CAR) spatial model-based approach to impute missing values, making the model fit into the integrated nested Laplace approximation (INLA) framework. Combining the advantages of both the Markov chain Monte Carlo (MCMC) and INLA frameworks, the MCMCINLA algorithm is used to implement imputation of the missing data and fit the model to derive estimates of the parameters from the posterior margins. Finally, the economic data and the hemorrhagic fever with renal syndrome (HFRS) disease data of mainland China from 2016–2018 are used as examples to explore the development of public health in China in the post-epidemic era. The results show that compared with expectation maximization (EM) and full information maximum likelihood estimation (FIML), the predicted values of the missing data obtained using our method are closer to the true values, and the spatial distribution of HFRS in China can be inferred from the imputation results with a southern-heavy and northern-light distribution. It can provide some references for the development of public health in China in the post-epidemic era.     

Statistical Inference of the Generalized Inverted Exponential Distribution under Joint Progressively Type-II Censoring

In this paper, we study the statistical inference of the generalized inverted exponential distribution with the same scale parameter and various shape parameters based on joint progressively type-II censored data. The expectation maximization (EM) algorithm is applied to calculate the maximum likelihood estimates (MLEs) of the parameters. We obtain the observed information matrix based on the missing value principle. Interval estimations are computed by the bootstrap method. We provide Bayesian inference for the informative prior and the non-informative prior. The importance sampling technique is performed to derive the Bayesian estimates and credible intervals under the squared error loss function and the linex loss function, respectively. Eventually, we conduct the Monte Carlo simulation and real data analysis. Moreover, we consider the parameters that have order restrictions and provide the maximum likelihood estimates and Bayesian inference.     

Parameter inference in small world network disease models with approximate Bayesian Computational methods

Small world network models have been effective in capturing the variable behaviour of reported case data of the SARS coronavirus outbreak in Hong Kong during 2003. Simulations of these models have previously been realized using informed “guesses” of the proposed model parameters and tested for consistency with the reported data by surrogate analysis. In this paper we attempt to provide statistically rigorous parameter distributions using Approximate Bayesian Computation sampling methods. We find that such sampling schemes are a useful framework for fitting parameters of stochastic small world network models where simulation of the system is straightforward but expressing a likelihood is cumbersome.     

Effects of superspreaders in spread of epidemic

Within the standard SIR model with spatial structure, we propose two models for the superspreader. In one model, superspreaders have intrinsically strong infectiousness. In other model, they have many social connections. By Monte Carlo simulation, we obtain the percolation probability, the propagation speed, the epidemic curve, the distribution of secondary infected and the propagation path as functions of population and the density of superspreaders. By comparing the results with the data of SARS in Singapore 2003, we conclude that the latter model can explain the observation.     

A Bayesian Approach to the Estimation of Parameters and Their Interdependencies in Environmental Modeling

We present a case study for Bayesian analysis and proper representation of distributions and dependence among parameters when calibrating process-oriented environmental models. A simple water quality model for the Elbe River (Germany) is referred to as an example, but the approach is applicable to a wide range of environmental models with time-series output. Model parameters are estimated by Bayesian inference via Markov Chain Monte Carlo (MCMC) sampling. While the best-fit solution matches usual least-squares model calibration (with a penalty term for excessive parameter values), the Bayesian approach has the advantage of yielding a joint probability distribution for parameters. This posterior distribution encompasses all possible parameter combinations that produce a simulation output that fits observed data within measurement and modeling uncertainty. Bayesian inference further permits the introduction of prior knowledge, e.g., positivity of certain parameters. The estimated distribution shows to which extent model parameters are controlled by observations through the process of inference, highlighting issues that cannot be settled unless more information becomes available. An interactive interface enables tracking for how ranges of parameter values that are consistent with observations change during the process of a step-by-step assignment of fixed parameter values. Based on an initial analysis of the posterior via an undirected Gaussian graphical model, a directed Bayesian network (BN) is constructed. The BN transparently conveys information on the interdependence of parameters after calibration. Finally, a strategy to reduce the number of expensive model runs in MCMC sampling for the presented purpose is introduced based on a newly developed variant of delayed acceptance sampling with a Gaussian process surrogate and linear dimensionality reduction to support function-valued outputs.     

Quantifying the transmission potential of pandemic influenza

This article reviews quantitative methods to estimate the basic reproduction number of pandemic influenza, a key threshold quantity to help determine the intensity of interventions required to control the disease. Although it is difficult to assess the transmission potential of a probable future pandemic, historical epidemiologic data is readily available from previous pandemics, and as a reference quantity for future pandemic planning, mathematical and statistical analyses of historical data are crucial. In particular, because many historical records tend to document only the temporal distribution of cases or deaths (i.e. epidemic curve), our review focuses on methods to maximize the utility of time-evolution data and to clarify the detailed mechanisms of the spread of influenza.

First, we highlight structured epidemic models and their parameter estimation method which can quantify the detailed disease dynamics including those we cannot observe directly. Duration-structured epidemic systems are subsequently presented, offering firm understanding of the definition of the basic and effective reproduction numbers. When the initial growth phase of an epidemic is investigated, the distribution of the generation time is key statistical information to appropriately estimate the transmission potential using the intrinsic growth rate. Applications of stochastic processes are also highlighted to estimate the transmission potential using similar data. Critically important characteristics of influenza data are subsequently summarized, followed by our conclusions to suggest potential future methodological improvements.     

Maximum entropy approach to statistical inference for an ocean acoustic waveguide

A conditional probability distribution suitable for estimating the statistical properties of ocean seabed parameter values inferred from acoustic measurements is derived from a maximum entropy principle. The specification of the expectation value for an error function constrains the maximization of an entropy functional. This constraint determines the sensitivity factor (β) to the error function of the resulting probability distribution, which is a canonical form that provides a conservative estimate of the uncertainty of the parameter values. From the conditional distribution, marginal distributions for individual parameters can be determined from integration over the other parameters. The approach is an alternative to obtaining the posterior probability distribution without an intermediary determination of the likelihood function followed by an application of Bayes' rule. In this paper the expectation value that specifies the constraint is determined from the values of the error function for the model solutions obtained from a sparse number of data samples. The method is applied to ocean acoustic measurements taken on the New Jersey continental shelf. The marginal probability distribution for the values of the sound speed ratio at the surface of the seabed and the source levels of a towed source are examined for different geoacoustic model representations.     

Bifurcation and Stability Analysis of the Equilibrium States in Thermodynamic Systems in a Small Vicinity of the Equilibrium Values of Parameters

The dynamic behavior of thermodynamic system, described by one order parameter and one control parameter, in a small neighborhood of ordinary and bifurcation equilibrium values of the system parameters is studied. Using the general methods of investigating the branching (bifurcations) of solutions for nonlinear equations, we performed an exhaustive analysis of the order parameter dependences on the control parameter in a small vicinity of the equilibrium values of parameters, including the stability analysis of the equilibrium states, and the asymptotic behavior of the order parameter dependences on the control parameter (bifurcation diagrams). The peculiarities of the transition to an unstable state of the system are discussed, and the estimates of the transition time to the unstable state in the neighborhood of ordinary and bifurcation equilibrium values of parameters are given. The influence of an external field on the dynamic behavior of thermodynamic system is analyzed, and the peculiarities of the system dynamic behavior are discussed near the ordinary and bifurcation equilibrium values of parameters in the presence of external field. The dynamic process of magnetization of a ferromagnet is discussed by using the general methods of bifurcation and stability analysis presented in the paper.     

Effects of City-Size Heterogeneity on Epidemic Spreading in a Metapopulation: A Reaction-Diffusion Approach

We review and introduce a generalized reaction-diffusion approach to epidemic spreading in a metapopulation modeled as a complex network. The metapopulation consists of susceptible and infected individuals that are grouped in subpopulations symbolizing cities and villages that are coupled by human travel in a transportation network. By analytic methods and numerical simulations we calculate the fraction of infected people in the metapopulation in the long time limit, as well as the relevant parameters characterizing the epidemic threshold that separates an epidemic from a non-epidemic phase. Within this model, we investigate the effect of a heterogeneous network topology and a heterogeneous subpopulation size distribution. Such a system is suited for epidemic modeling where small villages and big cities exist simultaneously in the metapopulation. We find that the heterogeneous conditions cause the epidemic threshold to be a non-trivial function of the reaction rates (local parameters), the network’s topology (global parameters) and the cross-over population size that separates “village dynamics” from “city dynamics”.     

Unravelling the size distribution of social groups with information theory in complex networks

The minimization of Fisher’s information (MFI) approach of Frieden et al. [Phys. Rev. E 60, 48 (1999)] is applied to the study of size distributions in social groups on the basis of a recently established analogy between scale invariant systems and classical gases [Phys. A 389, 490 (2010)]. Going beyond the ideal gas scenario is seen to be tantamount to simulating the interactions taking place, for a competitive cluster growth process, in a scale-free ideal network – a non-correlated network with a connection-degree’s distribution that mimics the scale-free ideal gas density distribution. We use a scaling rule that allows one to classify the final cluster-size distributions using only one parameter that we call the competitiveness, which can be seen as a measure of the strength of the interactions. We find that both empirical city-size distributions and electoral results can be thus reproduced and classified according to this competitiveness-parameter, that also allow us to infer the maximum number of stable social relationships that one person can maintain, known as the Dunbar number, together with its standard deviation. We discuss the importance of this number in connection with the empirical phenomenon known as “six-degrees of separation”. Finally, we show that scaled city-size distributions of large countries follow, in general, the same universal distribution.     

在二部无标度网上的两性疾病传播

利用易感-感染-易感(SIS)传播模型研究人类性接触网上的病毒传播.当仅仅考虑异性性接触时,该网络是一个二部的无标度网.对这个网络上的SIS传播模型,通过率方程的方法分析了男性感染率和女性感染率与传染阈值之间的关系,发现女性感染者与男性感染者之比由网络的拓扑和男女感染率之比所确定.这一结果表明性接触网的拓扑对性传染病传播的重要性.最后给出了支持理论结果的数值模拟. 关键词： 性传染病 两性性接触网 无标度网络 二部图     

Disease spreading in structured scale-free networks

We study the spreading of a disease on top of structured scale-free networks recently introduced. By means of numerical simulations we analyze the SIS and the SIR models. Our results show that when the connectivity fluctuations of the network are unbounded whether the epidemic threshold exists strongly depends on the initial density of infected individuals and the type of epidemiological model considered. Analytical arguments are provided in order to account for the observed behavior. We conclude that the peculiar topological features of this network and the absence of small-world properties determine the dynamics of epidemic spreading. Received 16 October 2002 Published online 4 February 2003 RID="a" ID="a"e-mail: yamir@ictp.trieste.it     

Epidemic propagation on adaptive coevolutionary networks with preferential local-world reconnecting strategy

In the propagation of an epidemic in a population, individuals adaptively adjust their behavior to avoid the risk of an epidemic. Differently from existing studies where new links are established randomly, a local link is established preferentially in this paper. We propose a new preferentially reconnecting edge strategy depending on spatial distance (PR- SD). For the PR-SD strategy, the new link is established at random with probability p and in a shortest distance with the probability 1 p. We establish the epidemic model on an adaptive network using Cellular Automata, and demonstrate the effectiveness of the proposed model by numerical simulations. The results show that the smaller the value of parameter p, the more difficult the epidemic spread is. The PR-SD strategy breaks long-range links and establishes as many short-range links as possible, which causes the network efficiency to decrease quickly and the propagation of the epidemic is restrained effectively.     

Theory of solute clustering in materials for atom probe

Pseudo-binary solute clustering in crystals was modelled analytically using expressions for the site-occupation probabilities that depend on solute concentration, crystallography and nearest-neighbour short-range order. Up to a cluster-size of 10 solute atoms, theoretical random and non-random cluster-size distributions were calculated for diamond (Si), simple (Mn), body centred (Fe) and face centred (Al) cubic lattices and the hexagonal close-packed (Mg) lattice. These calculations were then used to generate simulations of atom probe data, by stochastically removing atoms to simulate the effect of detector efficiency. These simulations may be used to determine self-consistent clustering algorithm parameters, measure short range order parameters and recover the effect of detector efficiency on the observed frequency distributions.     

Characterization of complex behaviors of TCP/RED computer networks based on nonlinear time series analysis methods

Packet-level observations are representative of the high sensitivity of TCP/RED computer network behavior with respect to network/RED parameter variations. That is, while we do not have any control on network parameters, mis-choosing of the RED parameters results in complex non-periodic oscillations in the router queue length that may damage the Quality of Service requirements. Characterizing the nature of such behaviors, however, helps the network designers to modify the RED design method in order to achieve better overall performance. In this paper, we first investigate the effect of variations in different RED parameters on the network behavior and then seek for the origin of such complex behaviors. For this purpose, different linear and nonlinear time series analysis methods have been applied to long-duration ns-2 packet-level data traces of a homogeneous TCP/RED network. The results of the analysis confirm that the complex behavior of the network can be represented by a nonlinear stochastic second-order process and it is not due to a deterministic chaos or a non-stationarity in the network.     

基于贝叶斯方法的设备级电磁脉冲效应评估

在电磁脉冲效应试验中,由于所获得的效应数据量一般较少,利用经典的数理统计方法对效应阈值场强进行概率拟合非常困难。基于贝叶斯数理统计方法,对油气管道数据采集与监视控制系统的中心控制系统客户端的电磁脉冲效应数据拟合分析。选择了Weibull分布模型和正态分布模型作为假设模型,并依次求得这两种模型参数的先验分布、似然函数和后验分布。通过拟合优度检验,最后基于贝叶斯信息准则选择形状参数、尺度参数分别为8.87,21.11的Weibull模型作为更合理的阈值场强概率分布模型。     

Uncertainty estimation in simultaneous Bayesian tracking and environmental inversion

This paper develops a Bayesian approach for two related inverse problems: tracking an acoustic source when ocean environmental parameters are unknown, and determining environmental parameters using acoustic data from an unknown (moving) source. The formulation considers source and environmental parameters as unknown random variables constrained by noisy acoustic data and by prior information on parameter values (e.g., physical limits for environmental properties) and on inter-parameter relationships (limits on radial and vertical source speed). The goal is not simply to estimate parameter values, but to rigorously determine parameter uncertainty distributions, thereby quantifying the information content of the data/prior to resolve source and environmental parameters. Results are presented as marginal posterior probability densities (PPDs) for environmental parameters and joint marginal PPDs for source ranges and depths. Given the numerically intensive inversion, an efficient Markov-chain Monte Carlo importance-sampling approach is developed which combines Metropolis and heat-bath Gibbs' sampling, employs efficient proposal distributions based on a linearized PPD approximation, and considers nonunity sampling temperatures to ensure a complete parameter search. The approach is illustrated with two simulated examples representing tracking a quiet submerged source and geoacoustic inversion using noise from an unknown ship of opportunity. In both cases, source, seabed, and water-column parameters are unknown.     

Inference on COVID-19 Epidemiological Parameters Using Bayesian Survival Analysis

The need to provide accurate predictions in the evolution of the COVID-19 epidemic has motivated the development of different epidemiological models. These models require a careful calibration of their parameters to capture the dynamics of the phenomena and the uncertainty in the data. This work analyzes different parameters related to the personal evolution of COVID-19 (i.e., time of recovery, length of stay in hospital and delay in hospitalization). A Bayesian Survival Analysis is performed considering the age factor and period of the epidemic as fixed predictors to understand how these features influence the evolution of the epidemic. These results can be easily included in the epidemiological SIR model to make prediction results more stable.