The analysis of hospital infection data using hidden Markov models

Surveillance data for communicable nosocomial pathogens usually consist of short time series of low-numbered counts of infected patients. These often show overdispersion and autocorrelation. To date, almost all analyses of such data have ignored the communicable nature of the organisms and have used methods appropriate only for independent outcomes. Inferences that depend on such analyses cannot be considered reliable when patient-to-patient transmission is important. We propose a new method for analysing these data based on a mechanistic model of the epidemic process. Since important nosocomial pathogens are often carried asymptomatically with overt infection developing in only a proportion of patients, the epidemic process is usually only partially observed by routine surveillance data. We therefore develop a 'structured' hidden Markov model where the underlying Markov chain is generated by a simple transmission model. We apply both structured and standard (unstructured) hidden Markov models to time series for three important pathogens. We find that both methods can offer marked improvements over currently used approaches when nosocomial spread is important. Compared to the standard hidden Markov model, the new approach is more parsimonious, is more biologically plausible, and allows key epidemiological parameters to be estimated.     

Variational data assimilation with epidemic models

Mathematical modelling is playing an increasing role in developing an understanding of the dynamics of communicable disease and assisting the construction and implementation of intervention strategies. The threat of novel emergent pathogens in human and animal hosts implies the requirement for methods that can robustly estimate epidemiological parameters and provide forecasts. Here, a technique called variational data assimilation is introduced as a means of optimally melding dynamic epidemic models with epidemiological observations and data to provide forecasts and parameter estimates. Using data from a simulated epidemic process the method is used to estimate the start time of an epidemic, to provide a forecast of future epidemic behaviour and estimate the basic reproductive ratio. A feature of the method is that it uses a basic continuous-time SIR model, which is often the first point of departure for epidemiological modelling during the early stages of an outbreak. The method is illustrated by application to data gathered during an outbreak of influenza in a school environment.     

Universal risk phenotype of US counties for flu-like transmission to improve county-specific COVID-19 incidence forecasts

The spread of a communicable disease is a complex spatio-temporal process shaped by the specific transmission mechanism, and diverse factors including the behavior, socio-economic and demographic properties of the host population. While the key factors shaping transmission of influenza and COVID-19 are beginning to be broadly understood, making precise forecasts on case count and mortality is still difficult. In this study we introduce the concept of a universal geospatial risk phenotype of individual US counties facilitating flu-like transmission mechanisms. We call this the Universal Influenza-like Transmission (UnIT) score, which is computed as an information-theoretic divergence of the local incidence time series from an high-risk process of epidemic initiation, inferred from almost a decade of flu season incidence data gleaned from the diagnostic history of nearly a third of the US population. Despite being computed from the past seasonal flu incidence records, the UnIT score emerges as the dominant factor explaining incidence trends for the COVID-19 pandemic over putative demographic and socio-economic factors. The predictive ability of the UnIT score is further demonstrated via county-specific weekly case count forecasts which consistently outperform the state of the art models throughout the time-line of the COVID-19 pandemic. This study demonstrates that knowledge of past epidemics may be used to chart the course of future ones, if transmission mechanisms are broadly similar, despite distinct disease processes and causative pathogens.     

Bayesian inference for stochastic epidemic models with time-inhomogeneous removal rates

Stochastic compartmental models of the SEIR type are often used to make inferences on epidemic processes from partially observed data in which only removal times are available. For many epidemics, the assumption of constant removal rates is not plausible. We develop methods for models in which these rates are a time-dependent step function. A reversible jump MCMC algorithm is described that permits Bayesian inferences to be made on model parameters, particularly those associated with the step function. The method is applied to two datasets on outbreaks of smallpox and a respiratory disease. The analyses highlight the importance of allowing for time dependence by contrasting the predictive distributions for the removal times and comparing them with the observed data.      

Inferring the Source of Transmission with Phylogenetic Data

Identifying the source of transmission using pathogen genetic data is complicated by numerous biological, immunological, and behavioral factors. A large source of error arises when there is incomplete or sparse sampling of cases. Unsampled cases may act as either a common source of infection or as an intermediary in a transmission chain for hosts infected with genetically similar pathogens. It is difficult to quantify the probability of common source or intermediate transmission events, which has made it difficult to develop statistical tests to either confirm or deny putative transmission pairs with genetic data. We present a method to incorporate additional information about an infectious disease epidemic, such as incidence and prevalence of infection over time, to inform estimates of the probability that one sampled host is the direct source of infection of another host in a pathogen gene genealogy. These methods enable forensic applications, such as source-case attribution, for infectious disease epidemics with incomplete sampling, which is usually the case for high-morbidity community-acquired pathogens like HIV, Influenza and Dengue virus. These methods also enable epidemiological applications such as the identification of factors that increase the risk of transmission. We demonstrate these methods in the context of the HIV epidemic in Detroit, Michigan, and we evaluate the suitability of current sequence databases for forensic and epidemiological investigations. We find that currently available sequences collected for drug resistance testing of HIV are unlikely to be useful in most forensic investigations, but are useful for identifying transmission risk factors.     

A stochastic SIR model with contact-tracing: large population limits and statistical inference

This paper is devoted to the presentation and study of a specific stochastic epidemic model accounting for the effect of contact-tracing on the spread of an infectious disease. Precisely, one considers here the situation in which individuals identified as infected by the public health detection system may contribute to detecting other infectious individuals by providing information related to persons with whom they have had possibly infectious contacts. The control strategy, which consists of examining each individual who has been able to be identified on the basis of the information collected within a certain time period, is expected to efficiently reinforce the standard random-screening-based detection and considerably ease the epidemic. In the novel modelling of the spread of a communicable infectious disease considered here, the population of interest evolves through demographic, infection and detection processes, in a way that its temporal evolution is described by a stochastic Markov process, of which the component accounting for the contact-tracing feature is assumed to be valued in a space of point measures. For adequate scalings of the demographic, infection and detection rates, it is shown to converge to the weak deterministic solution of a PDE system, as a parameter n, interpreted as the population size, roughly speaking, becomes larger. From the perspective of the analysis of infectious disease data, this approximation result may serve as a key tool for exploring the asymptotic properties of standard inference methods such as maximum likelihood estimation. We state preliminary statistical results in this context. Eventually, relations of the model with the available data of the HIV epidemic in Cuba, in which country a contact-tracing detection system has been set up since 1986, is investigated and numerical applications are carried out.     

The effect of superspreading on epidemic outbreak size distributions

Recently, evidence has been presented to suggest that there are significant heterogeneities in the transmission of communicable diseases. Here, a stochastic simulation model of an epidemic process that allows for these heterogeneities is used to demonstrate the potentially considerable effect that heterogeneity of transmission will have on epidemic outbreak size distributions. Our simulation results agree well with approximations gained from the theory of branching processes. Outbreak size distributions have previously been used to infer basic epidemiological parameters. We show that if superspreading does occur then such distributions must be interpreted with care. The simulation results are discussed in relation to measles epidemics in isolated populations and in predominantly urban scenarios. The effect of three different disease control policies on outbreak size distributions are shown for varying levels of heterogeneity and disease control effort.     

Estimation and inference of R0 of an infectious pathogen by a removal method

The basic reproductive ratio, R0, is a central quantity in the investigation and management of infectious pathogens. The standard model for describing stochastic epidemics is the continuous time epidemic birth-and-death process. The incidence data used to fit this model tend to be collected in discrete units (days, weeks, etc.), which makes model fitting, and estimation of R0 difficult. Discrete time epidemic models better match the time scale of data collection but make simplistic assumptions about the stochastic epidemic process. By investigating the nature of the assumptions of a discrete time epidemic model, we derive a bias corrected maximum likelihood estimate of R0 based on the chain binomial model. The resulting 'removal' estimators provide estimates of R0 and the initial susceptible population size from time series of infectious case counts. We illustrate the performance of the estimators on both simulated data and real epidemics. Lastly, we discuss methods to address data collected with observation error.     

Autoinfection in wheat leaf rust epidemics

Autoinfection (within-host inoculum transmission) allows plant pathogens locally to increase their density on an infected host. Estimating autoinfection is of particular importance in understanding epidemic development in host mixtures. More generally, autoinfection influences the rate of host colonization by the pathogen, as well as pathogen evolution. Despite its importance in epidemiological models, autoinfection has not yet been directly quantified. It was measured here on wheat (Triticum aestivum) leaves infected by a pathogenic fungus (Puccinia triticina). Autoinfection was measured either on inoculated leaves or by assessing the local progeny of spontaneous infections, and was described by a model of the form y = microx(alpha), where alpha accounts for host saturation and micro represents the pathogen multiplication rate resulting from autoinfection. It was shown that autoinfection resulted in typical patterns of disease aggregation at the leaf level and influenced lesion distribution in the crop during the first epidemic stages. The parameter micro was calculated by taking overdispersion of the data and density dependence into account. It was found that a single lesion produced between 50 and 200 offspring by autoinfection, within a pathogen generation. By taking into account environmental variability, it was possible to estimate autoinfection under optimal conditions for epidemic development.     

A stochastic SIR model with contact-tracing: large population limits and statistical inference

This paper is devoted to the presentation and study of a specific stochastic epidemic model accounting for the effect of contact-tracing on the spread of an infectious disease. Precisely, one considers here the situation in which individuals identified as infected by the public health detection system may contribute to detecting other infectious individuals by providing information related to persons with whom they have had possibly infectious contacts. The control strategy, which consists of examining each individual who has been able to be identified on the basis of the information collected within a certain time period, is expected to efficiently reinforce the standard random-screening-based detection and considerably ease the epidemic. In the novel modelling of the spread of a communicable infectious disease considered here, the population of interest evolves through demographic, infection and detection processes, in a way that its temporal evolution is described by a stochastic Markov process, of which the component accounting for the contact-tracing feature is assumed to be valued in a space of point measures. For adequate scalings of the demographic, infection and detection rates, it is shown to converge to the weak deterministic solution of a PDE system, as a parameter n, interpreted as the population size, roughly speaking, becomes larger. From the perspective of the analysis of infectious disease data, this approximation result may serve as a key tool for exploring the asymptotic properties of standard inference methods such as maximum likelihood estimation. We state preliminary statistical results in this context. Eventually, relations of the model with the available data of the HIV epidemic in Cuba, in which country a contact-tracing detection system has been set up since 1986, is investigated and numerical applications are carried out.     

Costs and benefits of group living with disease: a case study of pneumonia in bighorn lambs (Ovis canadensis)

Group living facilitates pathogen transmission among social hosts, yet temporally stable host social organizations can actually limit transmission of some pathogens. When there are few between-subpopulation contacts for the duration of a disease event, transmission becomes localized to subpopulations. The number of per capita infectious contacts approaches the subpopulation size as pathogen infectiousness increases. Here, we illustrate that this is the case during epidemics of highly infectious pneumonia in bighorn lambs (Ovis canadensis). We classified individually marked bighorn ewes into disjoint seasonal subpopulations, and decomposed the variance in lamb survival to weaning into components associated with individual ewes, subpopulations, populations and years. During epidemics, lamb survival varied substantially more between ewe-subpopulations than across populations or years, suggesting localized pathogen transmission. This pattern of lamb survival was not observed during years when disease was absent. Additionally, group sizes in ewe-subpopulations were independent of population size, but the number of ewe-subpopulations increased with population size. Consequently, although one might reasonably assume that force of infection for this highly communicable disease scales with population size, in fact, host social behaviour modulates transmission such that disease is frequency-dependent within populations, and some groups remain protected during epidemic events.     

New insights into the evolutionary rate of HIV-1 at the within-host and epidemiological levels

Over calendar time, HIV-1 evolves considerably faster within individuals than it does at the epidemic level. This is a surprising observation since, from basic population genetic theory, we would expect the genetic substitution rate to be similar across different levels of biological organization. Three different mechanisms could potentially cause the observed mismatch in phylogenetic rates of divergence: temporal changes in selection pressure during the course of infection; frequent reversion of adaptive mutations after transmission; and the storage of the virus in the body followed by the preferential transmission of stored ancestral virus. We evaluate each of these mechanisms to determine whether they are likely to make a major contribution to the mismatch in phylogenetic rates. We conclude that the cycling of the virus through very long-lived memory CD4(+) T cells, a process that we call 'store and retrieve', is probably the major contributing factor to the rate mismatch. The preferential transmission of ancestral virus needs to be integrated into evolutionary models if we are to accurately predict the evolution of immune escape, drug resistance and virulence in HIV-1 at the population level. Moreover, early infection viruses should be the major target for vaccine design, because these are the viral strains primarily involved in transmission.     

Two-phase importance sampling for inference about transmission trees

There has been growing interest in the statistics community to develop methods for inferring transmission pathways of infectious pathogens from molecular sequence data. For many datasets, the computational challenge lies in the huge dimension of the missing data. Here, we introduce an importance sampling scheme in which the transmission trees and phylogenies of pathogens are both sampled from reasonable importance distributions, alleviating the inference. Using this approach, arbitrary models of transmission could be considered, contrary to many earlier proposed methods. We illustrate the scheme by analysing transmissions of Streptococcus pneumoniae from household to household within a refugee camp, using data in which only a fraction of hosts is observed, but which is still rich enough to unravel the within-household transmission dynamics and pairs of households between whom transmission is plausible. We observe that while probability of direct transmission is low even for the most prominent cases of transmission, still those pairs of households are geographically much closer to each other than expected under random proximity.     

天然草地管理措施对植物病害的影响研究进展

放牧、围封、刈割和焚烧是天然草地管理的最主要方式,植物病害是草地生产力的主要限制因素之一,综合考虑生态和经济效益,探讨利用方式对天然草地植物病害的影响,进而采取合理的管理措施,有效降低草地病害危害、提高草地生产力和生态服务功能。分析了放牧、围封和焚烧等草原管理措施对植物病害的影响。放牧对草地植物病害的发生有双重影响,对多数病害而言,放牧可清除草地植被中的病株,减少初侵染源而降低植物病害的发生;但对物理传播的病害,放牧通过家畜传播病原侵染植物,导致病害大面积发生。刈割阻止真菌的进一步侵入与定殖,从而减少草地病害的发生机会;另一方面,刈割形成有利于病原真菌孢子传播的条件,病原真菌通过刈割工具传播到刈割造成的叶片伤口上,为侵入植物体内提供了方便。草地围封增加了植物物种的多度同时降低植物多样性,有利于病害发生。冬末春初植被返青前,焚烧草地可清除枯枝落叶,减少越冬的病原物,降低病害的发生。同时对该领域的研究进行了展望,对今后研究提出了建议。     

Optimization of Proteomic Sample Preparation Procedures for Comprehensive Protein Characterization of Pathogenic Systems

Mass spectrometry-based proteomics is a powerful analytical tool for investigating pathogens and their interactions within a host. The sensitivity of such analyses provides broad proteome characterization, but the sample-handling procedures must first be optimized to ensure compatibility with the technique and to maximize the dynamic range of detection. The decision-making process for determining optimal growth conditions, preparation methods, sample analysis methods, and data analysis techniques in our laboratory is discussed herein with consideration of the balance in sensitivity, specificity, and biomass losses during analysis of host-pathogen systems.     

A Bayesian Inference Framework to Reconstruct Transmission Trees Using Epidemiological and Genetic Data

The accurate identification of the route of transmission taken by an infectious agent through a host population is critical to understanding its epidemiology and informing measures for its control. However, reconstruction of transmission routes during an epidemic is often an underdetermined problem: data about the location and timings of infections can be incomplete, inaccurate, and compatible with a large number of different transmission scenarios. For fast-evolving pathogens like RNA viruses, inference can be strengthened by using genetic data, nowadays easily and affordably generated. However, significant statistical challenges remain to be overcome in the full integration of these different data types if transmission trees are to be reliably estimated. We present here a framework leading to a bayesian inference scheme that combines genetic and epidemiological data, able to reconstruct most likely transmission patterns and infection dates. After testing our approach with simulated data, we apply the method to two UK epidemics of Foot-and-Mouth Disease Virus (FMDV): the 2007 outbreak, and a subset of the large 2001 epidemic. In the first case, we are able to confirm the role of a specific premise as the link between the two phases of the epidemics, while transmissions more densely clustered in space and time remain harder to resolve. When we consider data collected from the 2001 epidemic during a time of national emergency, our inference scheme robustly infers transmission chains, and uncovers the presence of undetected premises, thus providing a useful tool for epidemiological studies in real time. The generation of genetic data is becoming routine in epidemiological investigations, but the development of analytical tools maximizing the value of these data remains a priority. Our method, while applied here in the context of FMDV, is general and with slight modification can be used in any situation where both spatiotemporal and genetic data are available.     

Transmission or Within-Host Dynamics Driving Pulses of Zoonotic Viruses in Reservoir–Host Populations

Progress in combatting zoonoses that emerge from wildlife is often constrained by limited knowledge of the biology of pathogens within reservoir hosts. We focus on the host–pathogen dynamics of four emerging viruses associated with bats: Hendra, Nipah, Ebola, and Marburg viruses. Spillover of bat infections to humans and domestic animals often coincides with pulses of viral excretion within bat populations, but the mechanisms driving such pulses are unclear. Three hypotheses dominate current research on these emerging bat infections. First, pulses of viral excretion could reflect seasonal epidemic cycles driven by natural variations in population densities and contact rates among hosts. If lifelong immunity follows recovery, viruses may disappear locally but persist globally through migration; in either case, new outbreaks occur once births replenish the susceptible pool. Second, epidemic cycles could be the result of waning immunity within bats, allowing local circulation of viruses through oscillating herd immunity. Third, pulses could be generated by episodic shedding from persistently infected bats through a combination of physiological and ecological factors. The three scenarios can yield similar patterns in epidemiological surveys, but strategies to predict or manage spillover risk resulting from each scenario will be different. We outline an agenda for research on viruses emerging from bats that would allow for differentiation among the scenarios and inform development of evidence-based interventions to limit threats to human and animal health. These concepts and methods are applicable to a wide range of pathogens that affect humans, domestic animals, and wildlife.     

Dynamic health policies for controlling the spread of emerging infections: influenza as an example

The recent appearance and spread of novel infectious pathogens provide motivation for using models as tools to guide public health decision-making. Here we describe a modeling approach for developing dynamic health policies that allow for adaptive decision-making as new data become available during an epidemic. In contrast to static health policies which have generally been selected by comparing the performance of a limited number of pre-determined sequences of interventions within simulation or mathematical models, dynamic health policies produce "real-time" recommendations for the choice of the best current intervention based on the observable state of the epidemic. Using cumulative real-time data for disease spread coupled with current information about resource availability, these policies provide recommendations for interventions that optimally utilize available resources to preserve the overall health of the population. We illustrate the design and implementation of a dynamic health policy for the control of a novel strain of influenza, where we assume that two types of intervention may be available during the epidemic: (1) vaccines and antiviral drugs, and (2) transmission reducing measures, such as social distancing or mask use, that may be turned "on" or "off" repeatedly during the course of epidemic. In this example, the optimal dynamic health policy maximizes the overall population's health during the epidemic by specifying at any point of time, based on observable conditions, (1) the number of individuals to vaccinate if vaccines are available, and (2) whether the transmission-reducing intervention should be either employed or removed.     

Bacterial colonization and extinction on marine aggregates: stochastic model of species presence and abundance

Organic aggregates provide a favorable habitat for aquatic microbes, are efficiently filtered by shellfish, and may play a major role in the dynamics of aquatic pathogens. Quantifying this role requires understanding how pathogen abundance in the water and aggregate size interact to determine the presence and abundance of pathogen cells on individual aggregates. We build upon current understanding of the dynamics of bacteria and bacterial grazers on aggregates to develop a model for the dynamics of a bacterial pathogen species. The model accounts for the importance of stochasticity and the balance between colonization and extinction. Simulation results suggest that while colonization increases linearly with background density and aggregate size, extinction rates are expected to be nonlinear on small aggregates in a low background density of the pathogen. Under these conditions, we predict lower probabilities of pathogen presence and reduced abundance on aggregates compared with predictions based solely on colonization. These results suggest that the importance of aggregates to the dynamics of aquatic bacterial pathogens may be dependent on the interaction between aggregate size and background pathogen density, and that these interactions are strongly influenced by ecological interactions and pathogen traits. The model provides testable predictions and can be a useful tool for exploring how species‐specific differences in pathogen traits may alter the effect of aggregates on disease transmission.     

Is horizontal transmission really a problem for phylogenetic comparative methods? A simulation study using continuous cultural traits

Phylogenetic comparative methods (PCMs) provide a potentially powerful toolkit for testing hypotheses about cultural evolution. Here, we build on previous simulation work to assess the effect horizontal transmission between cultures has on the ability of both phylogenetic and non-phylogenetic methods to make inferences about trait evolution. We found that the mode of horizontal transmission of traits has important consequences for both methods. Where traits were horizontally transmitted separately, PCMs accurately reported when trait evolution was not correlated even at the highest levels of horizontal transmission. By contrast, linear regression analyses often incorrectly concluded that traits were correlated. Where simulated trait evolution was not correlated and traits were horizontally transmitted as a pair, both methods inferred increased levels of positive correlation with increasing horizontal transmission. Where simulated trait evolution was correlated, increasing rates of separate horizontal transmission led to decreasing levels of inferred correlation for both methods, but increasing rates of paired horizontal transmission did not. Furthermore, the PCM was also able to make accurate inferences about the ancestral state of traits. These results suggest that under certain conditions, PCMs can be robust to the effects of horizontal transmission. We discuss ways that future work can investigate the mode and tempo of horizontal transmission of cultural traits.