Data-based stochastic subgrid-scale parametrization: an approach using cluster-weighted modelling

A new approach for data-based stochastic parametrization of unresolved scales and processes in numerical weather and climate prediction models is introduced. The subgrid-scale model is conditional on the state of the resolved scales, consisting of a collection of local models. A clustering algorithm in the space of the resolved variables is combined with statistical modelling of the impact of the unresolved variables. The clusters and the parameters of the associated subgrid models are estimated simultaneously from data. The method is implemented and explored in the framework of the Lorenz '96 model using discrete Markov processes as local statistical models. Performance of the cluster-weighted Markov chain scheme is investigated for long-term simulations as well as ensemble prediction. It clearly outperforms simple parametrization schemes and compares favourably with another recently proposed subgrid modelling scheme also based on conditional Markov chains.     

Essential epidemiological mechanisms underpinning the transmission dynamics of seasonal influenza

Seasonal influenza has considerable impact around the world, both economically and in mortality among risk groups, but there is considerable uncertainty as to the essential mechanisms and their parametrization. In this paper, we identify a number of characteristic features of influenza incidence time series in temperate regions, including ranges of annual attack rates and outbreak durations. By constraining the output of simple models to match these characteristic features, we investigate the role played by population heterogeneity, multiple strains, cross-immunity and the rate of strain evolution in the generation of incidence time series. Results indicate that an age-structured model with non-random mixing and co-circulating strains are both required to match observed time-series data. Our work gives estimates of the seasonal peak basic reproduction number, R₀, in the range 1.6–3. Estimates of R₀ are strongly correlated with the timescale for waning of immunity to current circulating seasonal influenza strain, which we estimate is between 3 and 8 years. Seasonal variation in transmissibility is largely confined to 15–30% of its mean value. While population heterogeneity and cross-immunity are required mechanisms, the degree of heterogeneity and cross-immunity is not tightly constrained. We discuss our findings in the context of other work fitting to seasonal influenza data.     

A novel approach for predicting risk of vector-borne disease establishment in marginal temperate environments under climate change: West Nile virus in the UK

Vector-borne diseases (VBDs), such as dengue, Zika, West Nile virus (WNV) and tick-borne encephalitis, account for substantial human morbidity worldwide and have expanded their range into temperate regions in recent decades. Climate change has been proposed as a likely driver of past and future expansion, however, the complex ecology of host and vector populations and their interactions with each other, environmental variables and land-use changes makes understanding the likely impacts of climate change on VBDs challenging. We present an environmentally driven, stage-structured, host–vector mathematical modelling framework to address this challenge. We apply our framework to predict the risk of WNV outbreaks in current and future UK climates. WNV is a mosquito-borne arbovirus which has expanded its range in mainland Europe in recent years. We predict that, while risks will remain low in the coming two to three decades, the risk of WNV outbreaks in the UK will increase with projected temperature rises and outbreaks appear plausible in the latter half of this century. This risk will increase substantially if increased temperatures lead to increases in the length of the mosquito biting season or if European strains show higher replication at lower temperatures than North American strains.     

Predictions of tumour morphological stability and evaluation against experimental observations

The hallmark of malignant tumours is their spread into neighbouring tissue and metastasis to distant organs, which can lead to life threatening consequences. One of the defining characteristics of aggressive tumours is an unstable morphology, including the formation of invasive fingers and protrusions observed both in vitro and in vivo. In spite of extensive biological, clinical and modelling study and research at physical scales ranging from the molecular to the tissue, the driving dynamics of tumour invasiveness are not completely understood, partly because it is challenging to observe and study cancer as a multi-scale system. Mathematical modelling has been applied to provide further insights into these complex invasive and metastatic behaviours. Modelling a solid tumour as an incompressible fluid, we consider three possible constitutive relations to describe tumour growth, namely Darcy''s law, Stokes'' law and the combined Darcy–Stokes law. We study the tumour morphological stability described by each model and evaluate the consistency between theoretical model predictions and experimental data from in vitro three-dimensional multicellular tumour spheroids. The analysis reveals that the Stokes model is the most consistent with the experimental observations, and that it predicts our experimental tumour growth is marginally stable. We further show that it is feasible to extract parameter values from a limited set of data and create a self-consistent modelling framework that can be extended to the multi-scale study of cancer.     

Parameter estimation and prediction for the course of a single epidemic outbreak of a plant disease.

Many epidemics of plant diseases are characterized by large variability among individual outbreaks. However, individual epidemics often follow a well-defined trajectory which is much more predictable in the short term than the ensemble (collection) of potential epidemics. In this paper, we introduce a modelling framework that allows us to deal with individual replicated outbreaks, based upon a Bayesian hierarchical analysis. Information about 'similar' replicate epidemics can be incorporated into a hierarchical model, allowing both ensemble and individual parameters to be estimated. The model is used to analyse the data from a replicated experiment involving spread of Rhizoctonia solani on radish in the presence or absence of a biocontrol agent, Trichoderma viride. The rate of primary (soil-to-plant) infection is found to be the most variable factor determining the final size of epidemics. Breakdown of biological control in some replicates results in high levels of primary infection and increased variability. The model can be used to predict new outbreaks of disease based upon knowledge from a 'library' of previous epidemics and partial information about the current outbreak. We show that forecasting improves significantly with knowledge about the history of a particular epidemic, whereas the precision of hindcasting to identify the past course of the epidemic is largely independent of detailed knowledge of the epidemic trajectory. The results have important consequences for parameter estimation, inference and prediction for emerging epidemic outbreaks.     

Simple models for containment of a pandemic.

Stochastic simulations of network models have become the standard approach to studying epidemics. We show that many of the predictions of these models can also be obtained from simple classical deterministic compartmental models. We suggest that simple models may be a better way to plan for a threatening pandemic with location and parameters as yet unknown, reserving more detailed network models for disease outbreaks already underway in localities where the social networks are well identified.We formulate compartmental models to describe outbreaks of influenza and attempt to manage a disease outbreak by vaccination or antiviral treatment. The models give an important prediction that may not have been noticed in other models, namely that the number of doses of antiviral treatment required is extremely sensitive to the number of initial infectives. This suggests that the actual number of doses needed cannot be estimated with any degree of reliability. The model is applicable to pre-epidemic vaccination, such as annual vaccination programs in anticipation of an 'ordinary' influenza outbreak with limited drift, and as a combination of treatment both before and during an epidemic.     

Modelling the initial phase of an epidemic using incidence and infection network data: 2009 H1N1 pandemic in Israel as a case study

This paper presents new computational and modelling tools for studying the dynamics of an epidemic in its initial stages that use both available incidence time series and data describing the population''s infection network structure. The work is motivated by data collected at the beginning of the H1N1 pandemic outbreak in Israel in the summer of 2009. We formulated a new discrete-time stochastic epidemic SIR (susceptible-infected-recovered) model that explicitly takes into account the disease''s specific generation-time distribution and the intrinsic demographic stochasticity inherent to the infection process. Moreover, in contrast with many other modelling approaches, the model allows direct analytical derivation of estimates for the effective reproductive number (R_e) and of their credible intervals, by maximum likelihood and Bayesian methods. The basic model can be extended to include age–class structure, and a maximum likelihood methodology allows us to estimate the model''s next-generation matrix by combining two types of data: (i) the incidence series of each age group, and (ii) infection network data that provide partial information of ‘who-infected-who’. Unlike other approaches for estimating the next-generation matrix, the method developed here does not require making a priori assumptions about the structure of the next-generation matrix. We show, using a simulation study, that even a relatively small amount of information about the infection network greatly improves the accuracy of estimation of the next-generation matrix. The method is applied in practice to estimate the next-generation matrix from the Israeli H1N1 pandemic data. The tools developed here should be of practical importance for future investigations of epidemics during their initial stages. However, they require the availability of data which represent a random sample of the real epidemic process. We discuss the conditions under which reporting rates may or may not influence our estimated quantities and the effects of bias.     

SPACE–TIME SPECTRAL ELEMENT METHOD FOR OPTIMAL SLEWING OF A FLEXIBLE BEAM

A new computational approach to modelling and control of a flexible beam is proposed. The structural modelling and the control design problems are formulated in a unified mathematical framework that allows simultaneous structural and control design iterations that result in an optimal overall system performance. The method employs the space–time spectral elements for simultaneous space and time discretizations of a Timoshenko beam model. Dimensionless equations of motion are derived using Hamilton's principle of variable action and an integral formulation in the framework of space–time spectral elements is introduced. An optimal control problem formulated for the continuum model is transformed by the space–time spectral element formulation into an optimization problem in a finite-dimensional parameter space. Dynamic programming is then used to obtain both open and closed loop control laws. A simulation study shows good performance of the control law applied to the nominal model. It is also demonstrated that proper discretization yields performance robustness of the system with respect to modal truncation.     

Time and dose-dependent risk of pneumococcal pneumonia following influenza: a model for within-host interaction between influenza and Streptococcus pneumoniae

A significant fraction of seasonal and in particular pandemic influenza deaths are attributed to secondary bacterial infections. In animal models, influenza virus predisposes hosts to severe infection with both Streptococcus pneumoniae and Staphylococcus aureus. Despite its importance, the mechanistic nature of the interaction between influenza and pneumococci, its dependence on the timing and sequence of infections as well as the clinical and epidemiological consequences remain unclear. We explore an immune-mediated model of the viral–bacterial interaction that quantifies the timing and the intensity of the interaction. Taking advantage of the wealth of knowledge gained from animal models, and the quantitative understanding of the kinetics of pathogen-specific immunological dynamics, we formulate a mathematical model for immune-mediated interaction between influenza virus and S. pneumoniae in the lungs. We use the model to examine the pathogenic effect of inoculum size and timing of pneumococcal invasion relative to influenza infection, as well as the efficacy of antivirals in preventing severe pneumococcal disease. We find that our model is able to capture the key features of the interaction observed in animal experiments. The model predicts that introduction of pneumococcal bacteria during a 4–6 day window following influenza infection results in invasive pneumonia at significantly lower inoculum size than in hosts not infected with influenza. Furthermore, we find that antiviral treatment administered later than 4 days after influenza infection was not able to prevent invasive pneumococcal disease. This work provides a quantitative framework to study interactions between influenza and pneumococci and has the potential to accurately quantify the interactions. Such quantitative understanding can form a basis for effective clinical care, public health policies and pandemic preparedness.     

Epidemic cycles driven by host behaviour

Host immunity and demographics (the recruitment of susceptibles via birthrate) have been demonstrated to be a key determinant of the periodicity of measles, pertussis and dengue epidemics. However, not all epidemic cycles are from pathogens inducing sterilizing immunity or are driven by demographics. Many sexually transmitted infections are driven by sexual behaviour. We present a mathematical model of disease transmission where individuals can disconnect and reconnect depending on the infectious status of their contacts. We fit the model to historic syphilis (Treponema pallidum) and gonorrhea (Neisseria gonorrhoeae) incidence in the USA and explore potential intervention strategies against syphilis. We find that cycles in syphilis incidence can be driven solely by changing sexual behaviour in structured populations. Our model also explains the lack of similar cycles in gonorrhea incidence even if the two infections share the same propagation pathways. Our model similarly illustrates how sudden epidemic outbreaks can occur on time scales smaller than the characteristic demographic time scale of the population and that weaker infections can lead to more violent outbreaks. Behaviour also appears to be critical for control strategies as we found a bigger sensitivity to behavioural interventions than antibiotic treatment. Thus, behavioural interventions may play a larger role than previously thought, especially in the face of antibiotic resistance and low intervention efficacies.     

Bayesian random effect models incorporating real-time weather and traffic data to investigate mountainous freeway hazardous factors

Freeway crash occurrences are highly influenced by geometric characteristics, traffic status, weather conditions and drivers’ behavior. For a mountainous freeway which suffers from adverse weather conditions, it is critical to incorporate real-time weather information and traffic data in the crash frequency study. In this paper, a Bayesian inference method was employed to model one year's crash data on I-70 in the state of Colorado. Real-time weather and traffic variables, along with geometric characteristics variables were evaluated in the models. Two scenarios were considered in this study, one seasonal and one crash type based case. For the methodology part, the Poisson model and two random effect models with a Bayesian inference method were employed and compared in this study. Deviance Information Criterion (DIC) was utilized as a comparison factor. The correlated random effect models outperformed the others. The results indicate that the weather condition variables, especially precipitation, play a key role in the crash occurrence models. The conclusions imply that different active traffic management strategies should be designed based on seasons, and single-vehicle crashes have different crash mechanism compared to multi-vehicle crashes.     

Distributed supply chain network modelling and simulation: integration of agent-based distributed simulation and improved SCOR model

Agent-based distributed simulation is an efficient methodology for modelling and analysing such complex adaptive systems as dynamic supply chain networks. However, it lacks an acceptable generic standard. Supply chain operations reference (SCOR) model is a cross-functional framework widely accepted as an industry standard. It provides the standard processes, performance metrics, best practices and associated software functionalities for modelling, evaluating and improving supply chain networks. However, it is a static tool. Integration of agent-based distributed simulation and SCOR model can exploit their advantages to form a generic methodology for modelling and simulation of a wide range of supply chain networks. Therefore, this paper proposes a methodology for distributed supply chain network modelling and simulation by means of integration of agent-based distributed simulation and an improved SCOR model. The methodology contains two components: a hierarchical framework for modelling supply chain network based on the improved SCOR model and agent building blocks integrating the standard processes from the SCOR model. The hierarchical framework provides an approach for structure modelling in any level with different granularities based on the improved SCOR model, and allows rapidly mapping a supply chain network into the structure model of a multi-agent system; while agent building blocks are quite useful and convenient to fill the structure model to fulfil its function modelling. With the approach of structure modelling and function filling, not only can the process of agent-based supply chain network modelling be accelerated, but also the built models can be reused and expanded. Because the hierarchical framework is based on the conceptual framework of SCOR model and agent building blocks integrate the standard processes from SCOR model, the proposed methodology is more generic. In addition, the issues of sub-model synchronisation and data distribution management in the agent-based distributed simulation implementation are taken into consideration and the corresponding solutions for these issues are proposed. Finally, an example of a supply chain network is modelled and implemented to illustrate the proposed methodology and related solutions.     

Modelling cell motility and chemotaxis with evolving surface finite elements

We present a mathematical and a computational framework for the modelling of cell motility. The cell membrane is represented by an evolving surface, with the movement of the cell determined by the interaction of various forces that act normal to the surface. We consider external forces such as those that may arise owing to inhomogeneities in the medium and a pressure that constrains the enclosed volume, as well as internal forces that arise from the reaction of the cells'' surface to stretching and bending. We also consider a protrusive force associated with a reaction–diffusion system (RDS) posed on the cell membrane, with cell polarization modelled by this surface RDS. The computational method is based on an evolving surface finite-element method. The general method can account for the large deformations that arise in cell motility and allows the simulation of cell migration in three dimensions. We illustrate applications of the proposed modelling framework and numerical method by reporting on numerical simulations of a model for eukaryotic chemotaxis and a model for the persistent movement of keratocytes in two and three space dimensions. Movies of the simulated cells can be obtained from http://homepages.warwick.ac.uk/∼maskae/CV_Warwick/Chemotaxis.html.     

Modelling biological behaviours with the unified modelling language: an immunological case study and critique

We present a framework to assist the diagrammatic modelling of complex biological systems using the unified modelling language (UML). The framework comprises three levels of modelling, ranging in scope from the dynamics of individual model entities to system-level emergent properties. By way of an immunological case study of the mouse disease experimental autoimmune encephalomyelitis, we show how the framework can be used to produce models that capture and communicate the biological system, detailing how biological entities, interactions and behaviours lead to higher-level emergent properties observed in the real world. We demonstrate how the UML can be successfully applied within our framework, and provide a critique of UML''s ability to capture concepts fundamental to immunology and biology more generally. We show how specialized, well-explained diagrams with less formal semantics can be used where no suitable UML formalism exists. We highlight UML''s lack of expressive ability concerning cyclic feedbacks in cellular networks, and the compounding concurrency arising from huge numbers of stochastic, interacting agents. To compensate for this, we propose several additional relationships for expressing these concepts in UML''s activity diagram. We also demonstrate the ambiguous nature of class diagrams when applied to complex biology, and question their utility in modelling such dynamic systems. Models created through our framework are non-executable, and expressly free of simulation implementation concerns. They are a valuable complement and precursor to simulation specifications and implementations, focusing purely on thoroughly exploring the biology, recording hypotheses and assumptions, and serve as a communication medium detailing exactly how a simulation relates to the real biology.     

Spatial dynamics of bar-headed geese migration in the context of H5N1

Virulent outbreaks of highly pathogenic avian influenza (HPAI) since 2005 have raised the question about the roles of migratory and wild birds in the transmission of HPAI. Despite increased monitoring, the role of wild waterfowl as the primary source of the highly pathogenic H5N1 has not been clearly established. The impact of outbreaks of HPAI among species of wild birds which are already endangered can nevertheless have devastating consequences for the local and non-local ecology where migratory species are established. Understanding the entangled dynamics of migration and the disease dynamics will be key to prevention and control measures for humans, migratory birds and poultry. Here, we present a spatial dynamic model of seasonal migration derived from first principles and linking the local dynamics during migratory stopovers to the larger scale migratory routes. We discuss the effect of repeated epizootic at specific migratory stopovers for bar-headed geese (Anser indicus). We find that repeated deadly outbreaks of H5N1 on stopovers during the autumn migration of bar-headed geese could lead to a larger reduction in the size of the equilibrium bird population compared with that obtained after repeated outbreaks during the spring migration. However, the opposite is true during the first few years of transition to such an equilibrium. The age-maturation process of juvenile birds which are more susceptible to H5N1 reinforces this result.     

Model validation: a systemic and systematic approach

The term ‘validation’ is used ubiquitously in association with the modelling activities of numerous disciplines including social, political, natural, physical sciences, and engineering. There is however, a wide range of definitions which give rise to very different interpretations of what activities the process involves. Analyses of results from the present large international effort in modelling radioactive waste disposal systems illustrate the urgent need to develop a common approach to model validation. Some possible explanations are offered to account for the present state of affairs. We believe that a rigorous approach to validation must necessarily be based on a thorough understanding and application of the theory of simulation and modelling. The methodology developed treats model validation and code verification in a systemic and systematic fashion. In fact, this approach may be regarded as a comprehensive framework to assess the adequacy of any simulation study.     

It wasn't supposed to be a coronavirus: The quest for an influenza A(H5N1)-derived vaccine and the limits of pandemic preparedness

The COVID-19 pandemic has raised questions about what efforts were made across the world to prepare governments and healthcare systems for such an event. This spotlight article looks at developments made in “pre-pandemic preparedness planning” following a number of outbreaks of influenza type A virus in 1997. At that time, a specific avian influenza subtype, referred to as A(H5N1), wreaked havoc among fowl but also infected humans through direct transmission. The potential for slight genetic mutations that could make A(H5N1) more infectious, allowing human-to-human transmission, presented the threat of a deadly influenza pandemic. As a result, the U.S. government (and others coordinating through the World Health Organization) launched a pandemic preparation plan, including strategies to develop vaccines against A(H5N1) and its genetic lineages each year. This spotlight article discusses the events that led to the specific concern about A(H5N1) among public health officials, as well as early efforts to derive and stockpile an appropriate vaccine to protect against a possible pandemic. This perspective presents the challenges the world has faced, in recent history, in striving to keep one step ahead of pandemic threats.     

A dynamic,ensemble learning approach to forecast dengue fever epidemic years in Brazil using weather and population susceptibility cycles

Transmission of dengue fever depends on a complex interplay of human, climate and mosquito dynamics, which often change in time and space. It is well known that its disease dynamics are highly influenced by multiple factors including population susceptibility to infection as well as by microclimates: small-area climatic conditions which create environments favourable for the breeding and survival of mosquitoes. Here, we present a novel machine learning dengue forecasting approach, which, dynamically in time and space, identifies local patterns in weather and population susceptibility to make epidemic predictions at the city level in Brazil, months ahead of the occurrence of disease outbreaks. Weather-based predictions are improved when information on population susceptibility is incorporated, indicating that immunity is an important predictor neglected by most dengue forecast models. Given the generalizability of our methodology to any location or input data, it may prove valuable for public health decision-making aimed at mitigating the effects of seasonal dengue outbreaks in locations globally.     

Managing engineering data for complex products

In this article we propose a design framework that integrates many application programs and manages the enormous quantity and variety of data generated while designing a complex product. Our discipline-independent framework provides data management services, such as version control and configuration management, needed by many engineering disciplines. This discipline-independent framework may be extended to satisfy the particular needs of specific engineering disciplines. The framework supports a message passing system and a flexible formula language, which facilitate the integration of design data from multiple disciplines.Our framework also includes powerful features for designing products with customer selectable options. First, we provide constructs, called option variables and option restrictions, for indicating what options are to be offered. Then, our option language allows designers to specify the product parametrically as a function of the option variables. Finally, we provide features for verifying that the design satisfies specified constraints for all combinations of options to be offered.