Effectiveness of non-pharmaceutical interventions to contain COVID-19: a case study of the 2020 spring pandemic wave in New York City

As COVID-19 continues to pose significant public health threats, quantifying the effectiveness of different public health interventions is crucial to inform intervention strategies. Using detailed epidemiological and mobility data available for New York City and comprehensive modelling accounting for under-detection, we reconstruct the COVID-19 transmission dynamics therein during the 2020 spring pandemic wave and estimate the effectiveness of two major non-pharmaceutical interventions—lockdown-like measures that reduce contact rates and universal masking. Lockdown-like measures were associated with greater than 50% transmission reduction for all age groups. Universal masking was associated with an approximately 7% transmission reduction overall and up to 20% reduction for 65+ year olds during the first month of implementation. This result suggests that face covering can substantially reduce transmission when lockdown-like measures are lifted but by itself may be insufficient to control SARS-CoV-2 transmission. Overall, findings support the need to implement multiple interventions simultaneously to effectively mitigate COVID-19 spread before the majority of population can be protected through mass-vaccination.     

Exogenous re-infection and the dynamics of tuberculosis epidemics: local effects in a network model of transmission

Infection with Mycobacterium tuberculosis leads to tuberculosis (TB) disease by one of the three possible routes: primary progression after a recent infection; re-activation of a latent infection; or exogenous re-infection of a previously infected individual. Recent studies show that optimal TB control strategies may vary depending on the predominant route to disease in a specific population. It is therefore important for public health policy makers to understand the relative frequency of each type of TB within specific epidemiological scenarios. Although molecular epidemiologic tools have been used to estimate the relative contribution of recent transmission and re-activation to the burden of TB disease, it is not possible to use these techniques to distinguish between primary disease and re-infection on a population level. Current estimates of the contribution of re-infection therefore rely on mathematical models which identify the parameters most consistent with epidemiological data; these studies find that exogenous re-infection is important only when TB incidence is high. A basic assumption of these models is that people in a population are all equally likely to come into contact with an infectious case. However, theoretical studies demonstrate that the social and spatial structure can strongly influence the dynamics of infectious disease transmission. Here, we use a network model of TB transmission to evaluate the impact of non-homogeneous mixing on the relative contribution of re-infection over realistic epidemic trajectories. In contrast to the findings of previous models, our results suggest that re-infection may be important in communities where the average disease incidence is moderate or low as the force of infection can be unevenly distributed in the population. These results have important implications for the development of TB control strategies.     

The role of heterogeneity in contact timing and duration in network models of influenza spread in schools

Influenza poses a significant health threat to children, and schools may play a critical role in community outbreaks. Mathematical outbreak models require assumptions about contact rates and patterns among students, but the level of temporal granularity required to produce reliable results is unclear. We collected objective contact data from students aged 5–14 at an elementary school and middle school in the state of Utah, USA, and paired those data with a novel, data-based model of influenza transmission in schools. Our simulations produced within-school transmission averages consistent with published estimates. We compared simulated outbreaks over the full resolution dynamic network with simulations on networks with averaged representations of contact timing and duration. For both schools, averaging the timing of contacts over one or two school days caused average outbreak sizes to increase by 1–8%. Averaging both contact timing and pairwise contact durations caused average outbreak sizes to increase by 10% at the middle school and 72% at the elementary school. Averaging contact durations separately across within-class and between-class contacts reduced the increase for the elementary school to 5%. Thus, the effect of ignoring details about contact timing and duration in school contact networks on outbreak size modelling can vary across different schools.     

Recent advances on the use of separated representations

Separated representations based on finite sum decompositions constitute an appealing strategy for reducing the computer resources and the calculation costs by reducing drastically the number of degrees of freedom that the functional approximations involve (the number of degrees of freedom scale linearly with the dimension of the space in which the model is defined instead of the exponential growing characteristic of mesh‐based discretization strategies). In our knowledge the use of separated representations is the only possibility for circumventing the terrific curse of dimensionality related to some highly multidimensional models involving hundreds of dimensions, as we proved in some of our former works. Its application is not restricted to multidimensional models, obviously separated representation can also be applied in standard 2D or 3D models, allowing for high resolution computations. Because its early life numerous issues persist, many of them attracting the curiosity of many research groups within the computational mechanics community. In this paper we are focusing in two issues never until now addressed: (i) the imposition of non‐homogenous essential boundary conditions and (ii) the consideration of complex geometries. Copyright © 2009 John Wiley & Sons, Ltd.     

Parametric topology optimization with multiresolution finite element models

We present a methodical procedure for topology optimization under uncertainty with multiresolution finite element (FE) models. We use our framework in a bifidelity setting where a coarse and a fine mesh corresponding to low- and high-resolution models are available. The inexpensive low-resolution model is used to explore the parameter space and approximate the parameterized high-resolution model and its sensitivity, where parameters are considered in both structural load and stiffness. We provide error bounds for bifidelity FE approximations and their sensitivities and conduct numerical studies to verify these theoretical estimates. We demonstrate our approach on benchmark compliance minimization problems, where we show significant reduction in computational cost for expensive problems such as topology optimization under manufacturing variability, reliability-based topology optimization, and three-dimensional topology optimization while generating almost identical designs to those obtained with a single-resolution mesh. We also compute the parametric von Mises stress for the generated designs via our bifidelity FE approximation and compare them with standard Monte Carlo simulations. The implementation of our algorithm, which extends the well-known 88-line topology optimization code in MATLAB, is provided.     

Some considerations on the treatment of uncertainties in risk assessment for practical decision making

This paper discusses the challenges involved in the representation and treatment of uncertainties in risk assessment, taking the point of view of its use in support to decision making. Two main issues are addressed: (1) how to faithfully represent and express the knowledge available to best support the decision making and (2) how to best inform the decision maker. A general risk-uncertainty framework is presented which provides definitions and interpretations of the key concepts introduced. The framework covers probability theory as well as alternative representations of uncertainty, including interval probability, possibility and evidence theory.     

Assessing the role of basic control measures, antivirals and vaccine in curtailing pandemic influenza: scenarios for the US, UK and the Netherlands

An increasing number of avian flu cases in humans, arising primarily from direct contact with poultry, in several regions of the world have prompted the urgency to develop pandemic preparedness plans worldwide. Leading recommendations in these plans include basic public health control measures for minimizing transmission in hospitals and communities, the use of antiviral drugs and vaccination. This paper presents a mathematical model for the evaluation of the pandemic flu preparedness plans of the United States (US), the United Kingdom (UK) and the Netherlands. The model is used to assess single and combined interventions. Using data from the US, we show that hospital and community transmission control measures alone can be highly effective in reducing the impact of a potential flu pandemic. We further show that while the use of antivirals alone could lead to very significant reductions in the burden of a pandemic, the combination of transmission control measures, antivirals and vaccine gives the most 'optimal' result. However, implementing such an optimal strategy at the onset of a pandemic may not be realistic. Thus, it is important to consider other plausible alternatives. An optimal preparedness plan is largely dependent on the availability of resources; hence, it is country-specific. We show that countries with limited antiviral stockpiles should emphasize their use therapeutically (rather than prophylactically). However, countries with large antiviral stockpiles can achieve greater reductions in disease burden by implementing them both prophylactically and therapeutically. This study promotes alternative strategies that may be feasible and attainable for the US, UK and the Netherlands. It emphasizes the role of hospital and community transmission control measures in addition to the timely administration of antiviral treatment in reducing the burden of a flu pandemic. The latter is consistent with the preparedness plans of the UK and the Netherlands. Our results indicate that for low efficacy and coverage levels of antivirals and vaccine, the use of a vaccine leads to the greatest reduction in morbidity and mortality compared with the singular use of antivirals. However, as these efficacy and coverage levels are increased, the use of antivirals is more effective.     

An Introduction to the Space Mapping Technique

The space mapping technique is intended for optimization of engineering models which involve very expensive function evaluations. It is assumed that two different models of the same physical system are available: Besides the expensive model of primary interest (denoted the fine model), access to a cheaper (coarse) model is assumed which may be less accurate.The main idea of the space mapping technique is to use the coarse model to gain information about the fine model, and to apply this in the search for an optimal solution of the latter. Thus the technique iteratively establishes a mapping between the parameters of the two models which relate similar model responses. Having this mapping, most of the model evaluations can be directed to the fast coarse model.In many cases this technique quickly provides an approximate optimal solution to the fine model that is sufficiently accurate for engineering purposes. Thus the space mapping technique may be considered a preprocessing technique that perhaps must be succeeded by use of classical optimization techniques. We present an automatic scheme which integrates the space mapping and classical techniques.     

Immunological heterogeneity informs estimation of the durability of vaccine protection

Deciphering the properties of vaccines against an emerging pathogen is essential for optimizing immunization strategies. Early after vaccine roll-out, however, uncertainties about vaccine immunity raise the question of how much time is needed to estimate these properties, particularly the durability of vaccine protection. Here we designed a simulation study, based on a generic transmission model of vaccination, to simulate the impact of a breadth of vaccines with different mean (range: 10 months–2 years) and variability (coefficient of variation range: 50–100%) of the duration of protection. Focusing on the dynamics of SARS-CoV-2 in the year after start of mass immunization in Germany as a case study, we then assessed how confidently the duration of protection could be estimated under a range of epidemiological scenarios. We found that lower mean and higher heterogeneity facilitated estimation of the duration of vaccine protection. Across the vaccines tested, rapid waning and high heterogeneity permitted complete identification of the duration of protection; by contrast, slow waning and low heterogeneity allowed only estimation of the fraction of vaccinees with rapid loss of immunity. These findings suggest that limited epidemiological data can inform the duration of vaccine immunity. More generally, they highlight the need to carefully consider immunological heterogeneity when designing transmission models to evaluate vaccines.     

Trade-offs between mobility restrictions and transmission of SARS-CoV-2

In their response to the COVID-19 outbreak, governments face the dilemma to balance public health and economy. Mobility plays a central role in this dilemma because the movement of people enables both economic activity and virus spread. We use mobility data in the form of counts of travellers between regions, to extend the often-used SEIR models to include mobility between regions. We quantify the trade-off between mobility and infection spread in terms of a single parameter, to be chosen by policy makers, and propose strategies for restricting mobility so that the restrictions are minimal while the infection spread is effectively limited. We consider restrictions where the country is divided into regions, and study scenarios where mobility is allowed within these regions, and disallowed between them. We propose heuristic methods to approximate optimal choices for these regions. We evaluate the obtained restrictions based on our trade-off. The results show that our methods are especially effective when the infections are highly concentrated, e.g. around a few municipalities, as resulting from superspreading events that play an important role in the spread of COVID-19. We demonstrate our method in the example of the Netherlands. The results apply more broadly when mobility data are available.     

Comparing approaches for modelling indirect contact transmission of infectious diseases

Mathematical models describing indirect contact transmission are an important component of infectious disease mitigation and risk assessment. A model that tracks microorganisms between compartments by coupled ordinary differential equations or a Markov chain is benchmarked against a mechanistic interpretation of the physical transfer of microorganisms from surfaces to fingers and subsequently to a susceptible person''s facial mucosal membranes. The primary objective was to compare these models in their estimates of doses and changes in microorganism concentrations on hands and fomites over time. The abilities of the models to capture the impact of episodic events, such as hand hygiene, and of contact patterns were also explored. For both models, greater doses were estimated for the asymmetrical scenarios in which a more contaminated fomite was touched more often. Differing representations of hand hygiene in the Markov model did not notably impact estimated doses but affected pathogen concentration dynamics on hands. When using the Markov model, losses due to hand hygiene should be handled as separate events as opposed to time-averaging expected losses. The discrete event model demonstrated the effect of hand-to-mouth contact timing on the dose. Understanding how model design influences estimated doses is important for advancing models as reliable risk assessment tools.     

Spatial connectivity in mosquito-borne disease models: a systematic review of methods and assumptions

Spatial connectivity plays an important role in mosquito-borne disease transmission. Connectivity can arise for many reasons, including shared environments, vector ecology and human movement. This systematic review synthesizes the spatial methods used to model mosquito-borne diseases, their spatial connectivity assumptions and the data used to inform spatial model components. We identified 248 papers eligible for inclusion. Most used statistical models (84.2%), although mechanistic are increasingly used. We identified 17 spatial models which used one of four methods (spatial covariates, local regression, random effects/fields and movement matrices). Over 80% of studies assumed that connectivity was distance-based despite this approach ignoring distant connections and potentially oversimplifying the process of transmission. Studies were more likely to assume connectivity was driven by human movement if the disease was transmitted by an Aedes mosquito. Connectivity arising from human movement was more commonly assumed in studies using a mechanistic model, likely influenced by a lack of statistical models able to account for these connections. Although models have been increasing in complexity, it is important to select the most appropriate, parsimonious model available based on the research question, disease transmission process, the spatial scale and availability of data, and the way spatial connectivity is assumed to occur.     

助推理论辅助公益服务设计发展探赜

目的 针对当前公益服务一定程度上缺乏可持续性的问题,旨在研究助推理论介入公益服务设计的可行性,总结适用于公益服务设计的助推策略。方法 首先,通过从服务提供者、服务核心及服务模式的角度将服务设计细分,依此对公益服务设计的概念进行界定,并按照服务对象资源的不同进行分类;其次,从服务对象行为的角度,将公益服务设计分为四个阶段,并依据福格行为模型分析阶段的行为要素,对助推原则进行阶段性划分;最后,分析现有不同类型的公益服务设计案例,验证各阶段可用的助推原则,并总结出从服务接触点出发的阶段性助推策略。结论 从理论与实际案例可以佐证助推理论与公益服务设计的良好适配性,助推理论为研究公益服务设计提供了新的思路,有利于促进服务流程实现的正向循环。     

Mode automata and their compilation into fault trees

In this article, we advocate the use of mode automata as a high level representation language for reliability studies. Mode automata are states/transitions based representations with the additional notion of flow. They can be seen as a generalization of both finite capacity Petri nets and block diagrams. They can be assembled into hierarchies by means of composition operations.The contribution of this article is twofold. First, we introduce mode automata and we discuss their relationship with other formalisms. Second, we propose an algorithm to compile mode automata into Boolean equations (fault trees). Such a compilation is of interest for two reasons. First, assessment tools for Boolean models are much more efficient than those for states/transitions models. Second, the automated generation of fault trees from higher level representations makes easier their maintenance through the life cycle of systems under study.     

Critical perspective on the consequences of the limited availability of kinetic data in metabolic dynamic modelling

Detailed kinetic models at the network reaction level are usually constructed using enzymatic mechanistic rate equations and the associated kinetic parameters. However, during the cellular life cycle thousands of different reactions occur, which makes it very difficult to build a detailed large-scale ldnetic model. In this work, we provide a critical overview of specific limitations found during the reconstruction of the central carbon metabolism dynamic model from E. coli (based on kinetic data available). In addition, we provide clues that will hopefully allow the systems biology community to more accurately construct metabolic dynamic models in the future. The difficulties faced during the construction of dynamic models are due not only to the lack of kinetic information but also to the fact that some data are still not curated. We hope that in the future, with the standardization of the in vitro enzyme protocols the approximation of in vitro conditions to the in vivo ones, it will be possible to integrate the available kinetic data into a complete large scale model. We also expect that collaborative projects between modellers and biologists will provide valuable kinetic data and permit the exchange of important information to solve most of these issues.     

Should we believe model predictions of future climate change?

Predictions of future climate are based on elaborate numerical computer models. As computational capacity increases and better observations become available, one would expect the model predictions to become more reliable. However, are they really improving, and how do we know? This paper discusses how current climate models are evaluated, why and where scientists have confidence in their models, how uncertainty in predictions can be quantified, and why models often tend to converge on what we observe but not on what we predict. Furthermore, it outlines some strategies on how the climate modelling community may overcome some of the current deficiencies in the attempt to provide useful information to the public and policy-makers.     

Use of Design Sensitivity Information in Response Surface and Kriging Metamodels

Metamodels based on responses from designed (numerical) experiments may form efficient approximations to functions in structural analysis. They can improve the efficiency of Engineering Optimization substantially by uncoupling computationally expensive analysis models and (iterative) optimization procedures. In this paper we focus on two strategies for building metamodels, namely Response Surface Methods (RSM) and kriging. We discuss key-concepts for both approaches, present strategies for model training and indicate ways to enhance these metamodeling approaches by including design sensitivity data. The latter may be advantageous in situations where information on design sensitivities is readily available, as is the case with e.g. Finite Element Models. Furthermore, we illustrate the use of RSM and kriging in a numerical model study and conclude with some remarks on their practical value.     

Performance analysis of multipath transmission over 802.11-based multihop ad hoc networks: a cross-layer perspective

Data transmission in ad hoc networks involves interactions between medium access control (MAC)-layer protocols and data forwarding along network-layer paths. These interactions have been shown to have a significant impact on the performance of a system. This impact on multipath data transmission over multihop IEEE 802.11 MAC-based ad hoc networks is assessed; analysis is from a cross-layer perspective. Both MAC layer protocols and network-layer data forwarding are taken into account in the system models. The frame service time at source in a 802.11 MAC-based multipath data transmission system under unsaturated conditions is studied. Analytical models are developed for two packet generation schemes (round robin and batch) with a Poisson frame arrival process. Moreover, an analytical model is developed to investigate the throughput of a multipath transmission system in 802.11-based multihop wireless networks. Two methods are proposed to estimate the impact of cross-layer interactions on the frame service time in such a system. Two bounds of the system throughput are obtained based on these estimation methods. These models are validated by means of simulation under various scenarios.