Modelling seasonal influenza: the role of weather and punctuated antigenic drift

Seasonal influenza appears as annual oscillations in temperate regions of the world, yet little is known as to what drives these annual outbreaks and what factors are responsible for their inter-annual variability. Recent studies suggest that weather variables, such as absolute humidity, are the key drivers of annual influenza outbreaks. The rapid, punctuated, antigenic evolution of the influenza virus is another major factor. We present a new framework for modelling seasonal influenza based on a discrete-time, age-of-infection, epidemic model, which allows the calculation of the model''s likelihood function in closed form. This framework may be used to perform model inference and parameter estimation rigorously. The modelling approach allows us to fit 11 years of Israeli influenza data, with the best models fitting the data with unusually high correlations in which r > 0.9. We show that using actual weather to modulate influenza transmission rate gives better results than using the inter-annual means of the weather variables, providing strong support for the role of weather in shaping the dynamics of influenza. This conclusion remains valid even when incorporating a more realistic depiction of the decay of immunity at the population level, which allows for discrete changes in immunity from year to year.     

Joint modelling of serological and hospitalization data reveals that high levels of pre-existing immunity and school holidays shaped the influenza A pandemic of 2009 in The Netherlands

Obtaining a quantitative understanding of the transmission dynamics of influenza A is important for predicting healthcare demand and assessing the likely impact of intervention measures. The pandemic of 2009 provides an ideal platform for developing integrative analyses as it has been studied intensively, and a wealth of data sources is available. Here, we analyse two complementary datasets in a disease transmission framework: cross-sectional serological surveys providing data on infection attack rates, and hospitalization data that convey information on the timing and duration of the pandemic. We estimate key epidemic determinants such as infection and hospitalization rates, and the impact of a school holiday. In contrast to previous approaches, our novel modelling of serological data with mixture distributions provides a probabilistic classification of individual samples (susceptible, immune and infected), propagating classification uncertainties to the transmission model and enabling serological classifications to be informed by hospitalization data. The analyses show that high levels of immunity among persons 20 years and older provide a consistent explanation of the skewed attack rates observed during the pandemic and yield precise estimates of the probability of hospitalization per infection (1–4 years: 0.00096 (95%CrI: 0.00078–0.0012); 5–19 years: 0.00036 (0.00031–0.0044); 20–64 years: 0.0015 (0.00091–0.0020); 65+ years: 0.0084 (0.0028–0.016)). The analyses suggest that in The Netherlands, the school holiday period reduced the number of infectious contacts between 5- and 9-year-old children substantially (estimated reduction: 54%; 95%CrI: 29–82%), thereby delaying the unfolding of the pandemic in The Netherlands by approximately a week.     

Modelling the spread of American foulbrood in honeybees

We investigate the spread of American foulbrood (AFB), a disease caused by the bacterium Paenibacillus larvae, that affects bees and can be extremely damaging to beehives. Our dataset comes from an inspection period carried out during an AFB epidemic of honeybee colonies on the island of Jersey during the summer of 2010. The data include the number of hives of honeybees, location and owner of honeybee apiaries across the island. We use a spatial SIR model with an underlying owner network to simulate the epidemic and characterize the epidemic using a Markov chain Monte Carlo (MCMC) scheme to determine model parameters and infection times (including undetected ‘occult’ infections). Likely methods of infection spread can be inferred from the analysis, with both distance- and owner-based transmissions being found to contribute to the spread of AFB. The results of the MCMC are corroborated by simulating the epidemic using a stochastic SIR model, resulting in aggregate levels of infection that are comparable to the data. We use this stochastic SIR model to simulate the impact of different control strategies on controlling the epidemic. It is found that earlier inspections result in smaller epidemics and a higher likelihood of AFB extinction.     

Dynamic survival analysis for non-Markovian epidemic models

We present a new method for analysing stochastic epidemic models under minimal assumptions. The method, dubbed dynamic survival analysis (DSA), is based on a simple yet powerful observation, namely that population-level mean-field trajectories described by a system of partial differential equations may also approximate individual-level times of infection and recovery. This idea gives rise to a certain non-Markovian agent-based model and provides an agent-level likelihood function for a random sample of infection and/or recovery times. Extensive numerical analyses on both synthetic and real epidemic data from foot-and-mouth disease in the UK (2001) and COVID-19 in India (2020) show good accuracy and confirm the method’s versatility in likelihood-based parameter estimation. The accompanying software package gives prospective users a practical tool for modelling, analysing and interpreting epidemic data with the help of the DSA approach.     

Which features of an outpatient treatment for COVID-19 would be most important for pandemic control? A modelling study

The global pandemic of coronavirus disease 2019 (COVID-19) has challenged healthcare systems worldwide. Lockdown, social distancing, and screening are thought to be the best means of stopping the virus from spreading and thus of preventing hospital capacity from being overloaded. However, it has also been suggested that effective outpatient treatment can control pandemics. We adapted a mathematical model of the beneficial effect of lockdown on viral transmission and used it to determine which characteristics of outpatient treatment would stop an epidemic. The data on confirmed cases, recovered cases, and deaths were collected from Santé Publique France. After defining components of the epidemic flow, we used a Morris global sensitivity analysis with a 10-level grid and 1000 trajectories to determine which of the treatment parameters had the largest effect. Treatment effectiveness was defined as a reduction in the patients'' contagiousness. Early treatment initiation was associated with better disease control—as long as the treatment was highly effective. However, initiation of a treatment with a moderate effectiveness rate (5%) after the peak of the epidemic was still better than poor distancing (i.e. when compliance with social distancing rules was below 60%). Even though most of today''s COVID-19 research is focused on inpatient treatment and vaccines, our results emphasize the potentially beneficial impact of even a moderately effective outpatient treatment on the current pandemic.     

Time‐invariant biological networks with feedback loops: structural equation models and structural identifiability

Quantitative analyses of biological networks such as key biological parameter estimation necessarily call for the use of graphical models. While biological networks with feedback loops are common in reality, the development of graphical model methods and tools that are capable of dealing with feedback loops is still in its infancy. Particularly, inadequate attention has been paid to the parameter identifiability problem for biological networks with feedback loops such that unreliable or even misleading parameter estimates may be obtained. In this study, the structural identifiability analysis problem of time‐invariant linear structural equation models (SEMs) with feedback loops is addressed, resulting in a general and efficient solution. The key idea is to combine Mason''s gain with Wright''s path coefficient method to generate identifiability equations, from which identifiability matrices are then derived to examine the structural identifiability of every single unknown parameter. The proposed method does not involve symbolic or expensive numerical computations, and is applicable to a broad range of time‐invariant linear SEMs with or without explicit latent variables, presenting a remarkable breakthrough in terms of generality. Finally, a subnetwork structure of the C. elegans neural network is used to illustrate the application of the authors’ method in practice.Inspec keywords: matrix algebra, least squares approximations, statistical analysis, parameter estimation, biologyOther keywords: structural identifiability analysis problem, time‐invariant linear structural equation models, feedback loops, identifiability equations, time‐invariant linear SEMs, time‐invariant biological networks, graphical model methods, parameter identifiability problem, biological parameter estimation, subnetwork structure, C. elegans neural network     

A multi-level modelling system for the design of flexible machining installations

Modern flexible manufacturing facilities can be highly complex, consisting of the latest developments in machine tool technology, automated material handling systems and sophisticated cell controllers. The design and management of such systems requires a large number of decisions and choices with regard to production mix, assignment of fixtures and cutting tools. A large number of commercial computer modelling packages are now available in the market place. Although these allow valuable assistance in the analysis of a manufacturing facility, they usually take significant amounts of time to build models and require a large amount of training, and can be constraining in their application. This paper establishes a research prototype for a multi-level approach for the realization of a three-phase design and modelling system for flexible machining facilities. It portrays the view of an integrated fully data-driven solution underpinned by a machining cell database, and outlines three major areas of work within the structure, i.e. the 'Cell Configurator', 'Evaluator' and 'Emulator'. The approach is demonstrated and supported throughout the paper by an industrial case study of a modern three-machine flexible machining cell, illustrating the use of the underlying methodology behind the approach and typical inputs/outputs at each phase. The final part of the paper provides a discussion of the approach adopted based on user comments and in relation to commercial simulation tools available.     

新冠隔离酒店零接触式寻路系统智创设计——以南京“宁归来首站公寓”为例

目的 以南京“宁归来首站公寓”为例,从防疫政策规范“零接触”的角度进行设计研究,打造隔离酒店寻路系统,提高用户对隔离酒店导视系统的寻路效率,降低因寻路造成交叉感染的风险,探索更适合疫情时代隔离酒店寻路系统的设计准则。方法 在深入研究防疫政策规范的基础上,结合“零接触”的设计理念对酒店内部寻路系统进行规划设计,并采用眼动追踪实验量化的方法进行验证,探究酒店内外部空间结构对隔离人员寻路行为的影响,进一步提高隔离人员的自主寻路效率。结果 对疫情初期隔离酒店寻路系统存在的缺陷进行对比分析,提出隔离酒店寻路系统的设计准则,并重新构建紧扣防疫政策规范的寻路系统设计。在对酒店内外部导视设置进行分析总结的基础上,解决疫情初期隔离酒店用户的寻路效率低、时间成本高以及易造成交叉感染风险等问题。结论 论证了隔离酒店新型导视系统的优势,为未来隔离酒店寻路方式及寻路设施新范式的创建提供了有益的参考。     

Systems engineering medicine: engineering the inflammation response to infectious and traumatic challenges

The complexity of the systemic inflammatory response and the lack of a treatment breakthrough in the treatment of pathogenic infection demand that advanced tools be brought to bear in the treatment of severe sepsis and trauma. Systems medicine, the translational science counterpart to basic science''s systems biology, is the interface at which these tools may be constructed. Rapid initial strides in improving sepsis treatment are possible through the use of phenomenological modelling and optimization tools for process understanding and device design. Higher impact, and more generalizable, treatment designs are based on mechanistic understanding developed through the use of physiologically based models, characterization of population variability, and the use of control-theoretic systems engineering concepts. In this review we introduce acute inflammation and sepsis as an example of just one area that is currently underserved by the systems medicine community, and, therefore, an area in which contributions of all types can be made.     

Toughening mechanisms in bioinspired multilayered materials

Outstanding mechanical properties of biological multilayered materials are strongly influenced by nanoscale features in their structure. In this study, mechanical behaviour and toughening mechanisms of abalone nacre-inspired multilayered materials are explored. In nacre''s structure, the organic matrix, pillars and the roughness of the aragonite platelets play important roles in its overall mechanical performance. A micromechanical model for multilayered biological materials is proposed to simulate their mechanical deformation and toughening mechanisms. The fundamental hypothesis of the model is the inclusion of nanoscale pillars with near theoretical strength (σ_th ~ E/30). It is also assumed that pillars and asperities confine the organic matrix to the proximity of the platelets, and, hence, increase their stiffness, since it has been previously shown that the organic matrix behaves more stiffly in the proximity of mineral platelets. The modelling results are in excellent agreement with the available experimental data for abalone nacre. The results demonstrate that the aragonite platelets, pillars and organic matrix synergistically affect the stiffness of nacre, and the pillars significantly contribute to the mechanical performance of nacre. It is also shown that the roughness induced interactions between the organic matrix and aragonite platelet, represented in the model by asperity elements, play a key role in strength and toughness of abalone nacre. The highly nonlinear behaviour of the proposed multilayered material is the result of distributed deformation in the nacre-like structure due to the existence of nano-asperities and nanopillars with near theoretical strength. Finally, tensile toughness is studied as a function of the components in the microstructure of nacre.     

Networks of influence and infection: parental choices and childhood disease

Clusters of unvaccinated individuals are at risk of outbreaks of infection. When an individual''s decision to choose vaccination is influenced by the choices of his social group, such clusters can readily arise. However, when the interactions that influence decision-making and those that permit the transmission of infection are different—for instance, when parents make vaccination decisions on behalf of their children—it is unclear how large the impact of this social influence will be. Here we use a modelling approach to represent social influence within a network of parents and the transmission of infection through a network of children. We show that the effect of social influence depends on the amount of overlap between the two different networks; large overlap means that clusters of parents who choose not to vaccinate are likely to have interacting children, generating clusters of unvaccinated children. Spatially local connections can further increase the impact of social influence. Outbreaks are most likely when parents who do not vaccinate have children who interact.     

Next-generation tools for evolutionary invasion analyses

Evolutionary invasion analysis is a powerful technique for modelling in evolutionary biology. The general approach is to derive an expression for the growth rate of a mutant allele encoding some novel phenotype, and then to use this expression to predict long-term evolutionary outcomes. Mathematically, such ‘invasion fitness’ expressions are most often derived using standard linear stability analyses from dynamical systems theory. Interestingly, there is a mathematically equivalent approach to such stability analyses that is often employed in mathematical epidemiology, and that is based on so-called ‘next-generation’ matrices. Although this next-generation matrix approach has sometimes also been used in evolutionary invasion analyses, it is not yet common in this area despite the fact that it can sometimes greatly simplify calculations. The aim of this article is to bring the approach to a wider evolutionary audience in two ways. First, we review the next-generation matrix approach and provide a novel, and easily intuited, interpretation of how this approach relates to more standard techniques. Second, we illustrate next-generation methods in evolutionary invasion analysis through a series of informative examples. Although focusing primarily on evolutionary invasion analysis, we provide several insights that apply to biological modelling in general.     

The cost of sensitive response and accurate adaptation in networks with an incoherent type-1 feed-forward loop

The incoherent type-1 feed-forward loop (I1-FFL) is ubiquitous in biological regulatory circuits. Although much is known about the functions of the I1-FFL motif, the energy cost incurred in the network and how it affects the performance of the network have not been investigated. Here, we study a generic I1-FFL enzymatic reaction network modelled after the GEF–GAP–Ras pathway responsible for chemosensory adaptation in eukaryotic cells. Our analysis shows that the I1-FFL network always operates out of equilibrium. Continuous energy dissipation is necessary to drive an internal phosphorylation–dephosphorylation cycle that is crucial in achieving strong short-time response and accurate long-time adaptation. In particular, we show quantitatively that the energy dissipated in the I1-FFL network is used (i) to increase the system''s initial response to the input signals; (ii) to enhance the adaptation accuracy at steady state; and (iii) to expand the range of such accurate adaptation. Moreover, we find that the energy dissipation rate, the catalytic speed and the maximum adaptation accuracy in the I1-FFL network satisfy the same energy–speed–accuracy relationship as in the negative-feedback-loop (NFL) networks. Because the I1-FFL and NFL are the only two basic network motifs that enable accurate adaptation, our results suggest that a universal cost–performance trade-off principle may underlie all cellular adaptation processes independent of the detailed biochemical circuit architecture.     

Correlation between protein secondary structure and mechanical performance for the ultra-tough dragline silk of Darwin's bark spider

The spider major ampullate (MA) silk exhibits high tensile strength and extensibility and is typically a blend of MaSp1 and MaSp2 proteins with the latter comprising glycine–proline–glycine–glycine-X repeating motifs that promote extensibility and supercontraction. The MA silk from Darwin''s bark spider (Caerostris darwini) is estimated to be two to three times tougher than the MA silk from other spider species. Previous research suggests that a unique MaSp4 protein incorporates proline into a novel glycine–proline–glycine–proline motif and may explain C. darwini MA silk''s extraordinary toughness. However, no direct correlation has been made between the silk''s molecular structure and its mechanical properties for C. darwini. Here, we correlate the relative protein secondary structure composition of MA silk from C. darwini and four other spider species with mechanical properties before and after supercontraction to understand the effect of the additional MaSp4 protein. Our results demonstrate that C. darwini MA silk possesses a unique protein composition with a lower ratio of helices (31%) and β-sheets (20%) than other species. Before supercontraction, toughness, modulus and tensile strength correlate with percentages of β-sheets, unordered or random coiled regions and β-turns. However, after supercontraction, only modulus and strain at break correlate with percentages of β-sheets and β-turns. Our study highlights that additional information including crystal size and crystal and chain orientation is necessary to build a complete structure–property correlation model.     

Impact of the implementation of rest days in live bird markets on the dynamics of H5N1 highly pathogenic avian influenza

Live bird markets (LBMs) act as a network ‘hub’ and potential reservoir of infection for domestic poultry. They may therefore be responsible for sustaining H5N1 highly pathogenic avian influenza (HPAI) virus circulation within the poultry sector, and thus a suitable target for implementing control strategies. We developed a stochastic transmission model to understand how market functioning impacts on the transmission dynamics. We then investigated the potential for rest days—periods during which markets are emptied and disinfected—to modulate the dynamics of H5N1 HPAI within the poultry sector using a stochastic meta-population model. Our results suggest that under plausible parameter scenarios, HPAI H5N1 could be sustained silently within LBMs with the time spent by poultry in markets and the frequency of introduction of new susceptible birds'' dominant factors determining sustained silent spread. Compared with interventions applied in farms (i.e. stamping out, vaccination), our model shows that frequent rest days are an effective means to reduce HPAI transmission. Furthermore, our model predicts that full market closure would be only slightly more effective than rest days to reduce transmission. Strategies applied within markets could thus help to control transmission of the disease.     

Identifying latent dynamic components in biological systems

In computational systems biology, the general aim is to derive regulatory models from multivariate readouts, thereby generating predictions for novel experiments. In the past, many such models have been formulated for different biological applications. The authors consider the scenario where a given model fails to predict a set of observations with acceptable accuracy and ask the question whether this is because of the model lacking important external regulations. Real‐world examples for such entities range from microRNAs to metabolic fluxes. To improve the prediction, they propose an algorithm to systematically extend the network by an additional latent dynamic variable which has an exogenous effect on the considered network. This variable''s time course and influence on the other species is estimated in a two‐step procedure involving spline approximation, maximum‐likelihood estimation and model selection. Simulation studies show that such a hidden influence can successfully be inferred. The method is also applied to a signalling pathway model where they analyse real data and obtain promising results. Furthermore, the technique can be employed to detect incomplete network structures.Inspec keywords: biology computing, RNA, splines (mathematics), maximum likelihood estimation, approximation theory, biochemistryOther keywords: latent dynamic components, biological systems, computational system biology, regulatory models, multivariate readouts, biological applications, external regulations, real‐world examples, microRNA, metabolic fluxes, latent dynamic variables, variable time course, two‐step procedure, spline approximation, maximum‐likelihood estimation, model selection, signalling pathway model, real data, incomplete network structures     

Integrating stochasticity and network structure into an epidemic model

While the foundations of modern epidemiology are based upon deterministic models with homogeneous mixing, it is being increasingly realized that both spatial structure and stochasticity play major roles in shaping epidemic dynamics. The integration of these two confounding elements is generally ascertained through numerical simulation. Here, for the first time, we develop a more rigorous analytical understanding based on pairwise approximations to incorporate localized spatial structure and diffusion approximations to capture the impact of stochasticity. Our results allow us to quantify, analytically, the impact of network structure on the variability of an epidemic. Using the susceptible–infectious–susceptible framework for the infection dynamics, the pairwise stochastic model is compared with the stochastic homogeneous-mixing (mean-field) model—although to enable a fair comparison the homogeneous-mixing parameters are scaled to give agreement with the pairwise dynamics. At equilibrium, we show that the pairwise model always displays greater variation about the mean, although the differences are generally small unless the prevalence of infection is low. By contrast, during the early epidemic growth phase when the level of infection is increasing exponentially, the pairwise model generally shows less variation.     

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.     

The impact of antiretroviral therapy on population-level virulence evolution of HIV-1

In HIV-infected patients, an individual''s set point viral load (SPVL) strongly predicts disease progression. Some think that SPVL is evolving, indicating that the virulence of the virus may be changing, but the data are not consistent. In addition, the widespread use of antiretroviral therapy (ART) has the potential to drive virulence evolution. We develop a simple deterministic model designed to answer the following questions: what are the expected patterns of virulence change in the initial decades of an epidemic? Could administration of ART drive changes in virulence evolution and, what is the potential size and direction of this effect? We find that even without ART we would not expect monotonic changes in average virulence. Transient decreases in virulence following the peak of an epidemic are not necessarily indicative of eventual evolution to avirulence. In the short term, we would expect widespread ART to cause limited downward pressure on virulence. In the long term, the direction of the effect is determined by a threshold condition, which we define. We conclude that, given the surpassing benefits of ART to the individual and in reducing onward transmission, virulence evolution considerations need have little bearing on how we treat.     

Lipid biophysics and/or soft matter-inspired approach for controlling enveloped virus infectivity

Proven as a natural barrier against viral infection, pulmonary surfactant phospholipids have a biophysical and immunological role within the respiratory system, acting against microorganisms including viruses. Enveloped viruses have, in common, an outer bilayer membrane that forms the underlying structure for viral membrane proteins to function in an optimal way to ensure infectivity. Perturbating the membrane of viruses using exogenous lipids can be envisioned as a generic way to reduce their infectivity. In this context, the potential of exogenous lipids to be used against enveloped virus infectivity would be indicated by the resulting physical stress imposed to the viral membrane, and conical lipids, i.e. lyso-lipids, would be expected to generate stronger biophysical disturbances. We confirm that when treated with lyso-lipids the infectivity three strains of influenza virus (avian H2N3, equine H3N8 or pandemic human influenza H1N1) is reduced by up to 99% in a cell-based model. By contrast, lipids with a similar head group but two aliphatic chains were less effective (reducing infection by only 40–50%). This work opens a new path to merge concepts from different research fields, i.e. ‘soft matter physics'' and virology.