Risk maps for the spread of highly pathogenic avian influenza in poultry

Devastating epidemics of highly contagious animal diseases such as avian influenza, classical swine fever, and foot-and-mouth disease underline the need for improved understanding of the factors promoting the spread of these pathogens. Here the authors present a spatial analysis of the between-farm transmission of a highly pathogenic H7N7 avian influenza virus that caused a large epidemic in The Netherlands in 2003. The authors developed a method to estimate key parameters determining the spread of highly transmissible animal diseases between farms based on outbreak data. The method allows for the identification of high-risk areas for propagating spread in an epidemiologically underpinned manner. A central concept is the transmission kernel, which determines the probability of pathogen transmission from infected to uninfected farms as a function of interfarm distance. The authors show how an estimate of the transmission kernel naturally provides estimates of the critical farm density and local reproduction numbers, which allows one to evaluate the effectiveness of control strategies. For avian influenza, the analyses show that there are two poultry-dense areas in The Netherlands where epidemic spread is possible, and in which local control measures are unlikely to be able to halt an unfolding epidemic. In these regions an epidemic can only be brought to an end by the depletion of susceptible farms by infection or massive culling. The analyses provide an estimate of the spatial range over which highly pathogenic avian influenza viruses spread between farms, and emphasize that control measures aimed at controlling such outbreaks need to take into account the local density of farms.     

Estimating Temporal Transmission Parameters from Infectious Disease Household Data, with Application to Taiwan SARS Data

Taking households having at least one infective as standard units and considering both a within-household infection rate and a global infection rate, we propose a Bayesian two level mixing S-I-R (susceptible-infective-removed) counting process model in which the transmission parameters may change over time and the parameters of interest are the within-household infection rate and the removal rate. Customized Markov chain Monte Carlo methods are developed for generating samples from the posterior distribution for inference purpose, based only on the removal times. The numerical performance of this method is examined in a simulation study. Applying this method to 2003 Taiwan SARS data, we find that the within-household infection rate decreases, the removal rate increases and their ratio is less than one and decreases significantly during the epidemic. This method allows the estimation of these parameters during the epidemic. For a rapidly transmitted disease, it provides a method to nearly real-time tracking of infection measures.     

The spread of HB virus infection in familial foci in a territory hyperendemic for hepatitis B

Epidemiological surveillance with the use of highly sensitive techniques for the indication of markers of hepatitis B (HB) virus infection in their dynamics has made it possible to find out that at a territory, hypersensitive for HB, along the existing high risk of this infection as the result of parenteral medical manipulations the intensive natural transmission of HB virus infection occurs under the conditions of everyday contacts with sources of the infection, patients with chronic forms of HB virus infection being of the highest epidemic importance. Under these conditions, children aged up to 7 years have been found to belong to the highest risk group. As a consequence, children of this age should be covered in future by specific preventive measures against HB. The spread of the epidemic process of HB virus infection in family foci is usually manifested by anicteric (usually not diagnosed) forms of this infection. All these circumstances make it expedient to develop antiepidemic and prophylactic measures in the foci of HB.     

Modelling the wind-borne spread of highly pathogenic avian influenza virus between farms

A quantitative understanding of the spread of contaminated farm dust between locations is a prerequisite for obtaining much-needed insight into one of the possible mechanisms of disease spread between farms. Here, we develop a model to calculate the quantity of contaminated farm-dust particles deposited at various locations downwind of a source farm and apply the model to assess the possible contribution of the wind-borne route to the transmission of Highly Pathogenic Avian Influenza virus (HPAI) during the 2003 epidemic in the Netherlands. The model is obtained from a Gaussian Plume Model by incorporating the dust deposition process, pathogen decay, and a model for the infection process on exposed farms. Using poultry- and avian influenza-specific parameter values we calculate the distance-dependent probability of between-farm transmission by this route. A comparison between the transmission risk pattern predicted by the model and the pattern observed during the 2003 epidemic reveals that the wind-borne route alone is insufficient to explain the observations although it could contribute substantially to the spread over short distance ranges, for example, explaining 24% of the transmission over distances up to 25 km.     

Understanding Spatio-Temporal Variability in the Reproduction Ratio of the Bluetongue (BTV-1) Epidemic in Southern Spain (Andalusia) in 2007 Using Epidemic Trees

Andalusia (Southern Spain) is considered one of the main routes of introduction of bluetongue virus (BTV) into Europe, evidenced by a devastating epidemic caused by BTV-1 in 2007. Understanding the pattern and the drivers of BTV-1 spread in Andalusia is critical for effective detection and control of future epidemics. A long-standing metric for quantifying the behaviour of infectious diseases is the case-reproduction ratio (R_t), defined as the average number of secondary cases arising from a single infected case at time t (for t>0). Here we apply a method using epidemic trees to estimate the between-herd case reproduction ratio directly from epidemic data allowing the spatial and temporal variability in transmission to be described. We then relate this variability to predictors describing the hosts, vectors and the environment to better understand why the epidemic spread more quickly in some regions or periods. The R_t value for the BTV-1 epidemic in Andalusia peaked in July at 4.6, at the start of the epidemic, then decreased to 2.2 by August, dropped below 1 by September (0.8), and by October it had decreased to 0.02. BTV spread was the consequence of both local transmission within established disease foci and BTV expansion to distant new areas (i.e. new foci), which resulted in a high variability in BTV transmission, not only among different areas, but particularly through time, which suggests that general control measures applied at broad spatial scales are unlikely to be effective. This high variability through time was probably due to the impact of temperature on BTV transmission, as evidenced by a reduction in the value of R_t by 0.0041 for every unit increase (day) in the extrinsic incubation period (EIP), which is itself directly dependent on temperature. Moreover, within the range of values at which BTV-1 transmission occurred in Andalusia (20.6°C to 29.5°C) there was a positive correlation between temperature and R_t values, although the relationship was not linear, probably as a result of the complex relationship between temperature and the different parameters affecting BTV transmission. R_t values for BTV-1 in Andalusia fell below the threshold of 1 when temperatures dropped below 21°C, a much higher threshold than that reported in other BTV outbreaks, such as the BTV-8 epidemic in Northern Europe. This divergence may be explained by differences in the adaptation to temperature of the main vectors of the BTV-1 epidemic in Andalusia (Culicoides imicola) compared those of the BTV-8 epidemic in Northern Europe (Culicoides obsoletus). Importantly, we found that BTV transmission (R_t value) increased significantly in areas with higher densities of sheep. Our analysis also established that control of BTV-1 in Andalusia was complicated by the simultaneous establishment of several distant foci at the start of the epidemic, which may have been caused by several independent introductions of infected vectors from the North of Africa. We discuss the implications of these findings for BTV surveillance and control in this region of Europe.     

Prediction and Control of Brucellosis Transmission of Dairy Cattle in Zhejiang Province,China

Brucellosis is a bacterial disease caused by brucella; mainly spread by direct contact transmission through the brucella carriers, or indirect contact transmission by the environment containing large quantities of bacteria discharged by the infected individuals. At the beginning of 21st century, the epidemic among dairy cows in Zhejiang province, began to come back and has become a localized prevalent epidemic. Combining the pathology of brucellosis, the reported positive data characteristics, and the feeding method in Zhejiang province, this paper establishes an dynamic model to excavate the internal transmission dynamics, fit the real disease situation, predict brucellosis tendency and assess control measures in dairy cows. By careful analysis, we give some quantitative results as follows. (1) The external input of dairy cows from northern areas may lead to high fluctuation of the number of the infectious cows in Zhejiang province that can reach several hundreds. In this case, the disease cannot be controlled and the infection situation cannot easily be predicted. Thus, this paper encourages cows farms to insist on self-supplying production of the dairy cows. (2) The effect of transmission rate of brucella in environment to dairy cattle on brucellosis spreading is greater than transmission rate of the infectious dairy cattle to susceptible cattle. The prevalence of the epidemic is mainly aroused by environment transmission. (3) Under certain circumstances, the epidemic will become a periodic phenomenon. (4) For Zhejiang province, besides measures that have already been adopted, sterilization times of the infected regions is suggested as twice a week, and should be combined with management of the birth rate of dairy cows to control brucellosis spread.     

Combining Epidemiological and Genetic Networks Signifies the Importance of Early Treatment in HIV-1 Transmission

Inferring disease transmission networks is important in epidemiology in order to understand and prevent the spread of infectious diseases. Reconstruction of the infection transmission networks requires insight into viral genome data as well as social interactions. For the HIV-1 epidemic, current research either uses genetic information of patients'' virus to infer the past infection events or uses statistics of sexual interactions to model the network structure of viral spreading. Methods for a reliable reconstruction of HIV-1 transmission dynamics, taking into account both molecular and societal data are still lacking. The aim of this study is to combine information from both genetic and epidemiological scales to characterize and analyse a transmission network of the HIV-1 epidemic in central Italy.We introduce a novel filter-reduction method to build a network of HIV infected patients based on their social and treatment information. The network is then combined with a genetic network, to infer a hypothetical infection transmission network. We apply this method to a cohort study of HIV-1 infected patients in central Italy and find that patients who are highly connected in the network have longer untreated infection periods. We also find that the network structures for homosexual males and heterosexual populations are heterogeneous, consisting of a majority of ‘peripheral nodes’ that have only a few sexual interactions and a minority of ‘hub nodes’ that have many sexual interactions. Inferring HIV-1 transmission networks using this novel combined approach reveals remarkable correlations between high out-degree individuals and longer untreated infection periods. These findings signify the importance of early treatment and support the potential benefit of wide population screening, management of early diagnoses and anticipated antiretroviral treatment to prevent viral transmission and spread. The approach presented here for reconstructing HIV-1 transmission networks can have important repercussions in the design of intervention strategies for disease control.     

Integrating genetic and epidemiological data to determine transmission pathways of foot-and-mouth disease virus

Estimating detailed transmission trees that reflect the relationships between infected individuals or populations during a disease outbreak often provides valuable insights into both the nature of disease transmission and the overall dynamics of the underlying epidemiological process. These trees may be based on epidemiological data that relate to the timing of infection and infectiousness, or genetic data that show the genetic relatedness of pathogens isolated from infected individuals. Genetic data are becoming increasingly important in the estimation of transmission trees of viral pathogens due to their inherently high mutation rate. Here, we propose a maximum-likelihood approach that allows epidemiological and genetic data to be combined within the same analysis to infer probable transmission trees. We apply this approach to data from 20 farms infected during the 2001 UK foot-and-mouth disease outbreak, using complete viral genome sequences from each infected farm and information on when farms were first estimated to have developed clinical disease and when livestock on these farms were culled. Incorporating known infection links due to animal movement prior to imposition of the national movement ban results in the reduction of the number of trees from 41472 that are consistent with the genetic data to 1728, of which just 4 represent more than 95% of the total likelihood calculated using a model that accounts for the epidemiological data. These trees differ in several ways from those constructed prior to the availability of genetic data.     

Transmission and control of African horse sickness in The Netherlands: a model analysis

African horse sickness (AHS) is an equine viral disease that is spread by Culicoides spp. Since the closely related disease bluetongue established itself in The Netherlands in 2006, AHS is considered a potential threat for the Dutch horse population. A vector-host model that incorporates the current knowledge of the infection biology is used to explore the effect of different parameters on whether and how the disease will spread, and to assess the effect of control measures. The time of introduction is an important determinant whether and how the disease will spread, depending on temperature and vector season. Given an introduction in the most favourable and constant circumstances, our results identify the vector-to-host ratio as the most important factor, because of its high variability over the country. Furthermore, a higher temperature accelerates the epidemic, while a higher horse density increases the extent of the epidemic. Due to the short infectious period in horses, the obvious clinical signs and the presence of non-susceptible hosts, AHS is expected to invade and spread less easily than bluetongue. Moreover, detection is presumed to be earlier, which allows control measures to be targeted towards elimination of infection sources. We argue that recommended control measures are euthanasia of infected horses with severe clinical signs and vector control in infected herds, protecting horses from midge bites in neighbouring herds, and (prioritized) vaccination of herds farther away, provided that transport regulations are strictly applied. The largest lack of knowledge is the competence and host preference of the different Culicoides species present in temperate regions.     

Dynamics of COVID-19 under social distancing measures are driven by transmission network structure

In the absence of pharmaceutical interventions, social distancing is being used worldwide to curb the spread of COVID-19. The impact of these measures has been inconsistent, with some regions rapidly nearing disease elimination and others seeing delayed peaks or nearly flat epidemic curves. Here we build a stochastic epidemic model to examine the effects of COVID-19 clinical progression and transmission network structure on the outcomes of social distancing interventions. Our simulations show that long delays between the adoption of control measures and observed declines in cases, hospitalizations, and deaths occur in many scenarios. We find that the strength of within-household transmission is a critical determinant of success, governing the timing and size of the epidemic peak, the rate of decline, individual risks of infection, and the success of partial relaxation measures. The structure of residual external connections, driven by workforce participation and essential businesses, interacts to determine outcomes. We suggest limited conditions under which the formation of household “bubbles” can be safe. These findings can improve future predictions of the timescale and efficacy of interventions needed to control second waves of COVID-19 as well as other similar outbreaks, and highlight the need for better quantification and control of household transmission.     

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.     

Assessing the Potential Impact of Hormonal-Based Contraceptives on HIV Transmission Dynamics Among Heterosexuals

HIV susceptibility linked to hormonal contraception (HC) has been studied before, but with mixed results. Reports from some of the recent findings have prompted the World Health Organisation to encourage women who use HC to concurrently use condoms in order to prevent HIV infection in the light of possible increased HIV risk of infection associated with hormone-based contraceptives. A two-sex HIV model classifying women into three risk groups consisting of individuals who use condoms, natural methods, and hormone-based contraceptives is formulated and analysed to assess the possible effects of various birth control strategies on the transmission dynamics of the disease. Our model results showed that women who use HC could be key drivers of the epidemic and that their increased infectivity may be critical in driving the epidemic. Women who use hormone-based contraceptives potentially act as a core group from which men get infected and in turn transmit the disease to other population groups. We fitted the model to HIV prevalence data for Zimbabwe reported by UNAIDS and Zimbabwe Ministry of Health and Child Care and used the model fit to project HIV prevalence. Predictions using HIV data for Zimbabwe suggest that a hypothesised increase in susceptibility and infectivity of two-, three-, and fourfold would result in a 25, 50, and 100% increase in baseline HIV prevalence projection, respectively, thus suggesting possible increased disease burden even in countries reporting plausible HIV prevalence declines. Although a possible causal relationship between HIV susceptibility and HC use remains subject of continuing scientific probe, its inclusion as part of birth control strategy has been shown in this study, to possibly increase HIV transmission. If proven, HC use may potentially explain the inordinate spread of HIV within the sub-Saharan Africa region and therefore compel for urgent assessment with a view to reorienting birth control methods in use in settings with generalised epidemics.     

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.     

Optimal isolation control strategies and cost-effectiveness analysis of a two-strain avian influenza model

The most important and effective measures against disease outbreaks in the absence of valid medicines or vaccine are quarantine and isolation strategies. In this paper optimal control theory is applied to a system of ordinary differential equation describing a two-strain avian influenza transmission via the Pontryagin's Maximum Principle. To this end, a pair of control variables representing the isolation strategies for individuals with avian and mutant strains were incorporated into the transmission model. The infection averted ratio (IAR) and the incremental cost-effectiveness ratio (ICER) were calculated to investigate the cost-effectiveness of all possible combinations of the control strategies. The simulation results show that the implementation of the combination strategy during the epidemic is the most cost-effective strategy for avian influenza transmission. This is followed by the control strategy involving isolation of individuals with the mutant strain. Also observed was the fact that low mutating and more virulent virus results in an increased control effort of isolating individuals with the avian strain; and high mutating with more virulent virus results in increased efforts in isolating individuals with the mutant strain.     

The number of links to and from the starting node as a predictor of epidemic size in small-size directed networks

Much recent modelling is focusing on epidemics in large-scale complex networks. Whether or not findings of these investigations also apply to networks of small size is still an open question. This is an important gap for many biological applications, including the spread of the oomycete pathogen Phytophthora ramorum in networks of plant nurseries. We use numerical simulations of disease spread and establishment in directed networks of 100 individual nodes at four levels of connectivity. Factors governing epidemic spread are network structure (local, small-world, random, scale-free) and the probabilities of infection persistence in a node and of infection transmission between connected nodes. Epidemic final size at equilibrium varies widely depending on the starting node of infection, although the latter does not affect the threshold condition for spread. The number of links from (out-degree) but not the number of links to (in-degree) the starting node of the epidemic explains a substantial amount of variation in final epidemic size at equilibrium irrespective of the structure of the network. The proportion of variance in epidemic size explained by the out-degree of the starting node increases with the level of connectivity. Targeting highly connected nodes is thus likely to make disease control more effective also in case of small-size populations, a result of relevance not just for the horticultural trade, but for epidemiology in general.     

Deterministic epidemic models with explicit household structure

For a wide range of airborne infectious diseases, transmission within the family or household is a key mechanism for the spread and persistence of infection. In general, household-based transmission is relatively strong but only involves a limited number of individuals in contact with each infectious person. In contrast, transmission outside the household can be characterised by many contacts but a lower probability of transmission. Here we develop a relatively simple dynamical model that captures these two transmission regimes. We compare the dynamics of such models for a range of household sizes, whilst constraining all models to have equal early growth rate so that all models fit to the same early incidence observations of an epidemic. Finally we consider the use of prophylactic vaccination, responsive vaccination, or antivirals to combat epidemic spread and focus on whether it is optimal to target controls at entire households or to treat individuals independently.     

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.     

A Mathematical Model of Intra-Colony Spread of American Foulbrood in European Honeybees (Apis mellifera L.)

American foulbrood (AFB) is one of the severe infectious diseases of European honeybees (Apis mellifera L.) and other Apis species. This disease is caused by a gram-positive, spore-forming bacterium Paenibacillus larvae. In this paper, a compartmental (SI framework) model is constructed to represent the spread of AFB within a colony. The model is analyzed to determine the long-term fate of the colony once exposed to AFB spores. It was found out that without effective and efficient treatment, AFB infection eventually leads to colony collapse. Furthermore, infection thresholds were predicted based on the stability of the equilibrium states. The number of infected cell combs is one of the factors that drive disease spread. Our results can be used to forecast the transmission timeline of AFB infection and to evaluate the control strategies for minimizing a possible epidemic.     

Predictions of COVID-19 dynamics in the UK: Short-term forecasting and analysis of potential exit strategies

Efforts to suppress transmission of SARS-CoV-2 in the UK have seen non-pharmaceutical interventions being invoked. The most severe measures to date include all restaurants, pubs and cafes being ordered to close on 20th March, followed by a “stay at home” order on the 23rd March and the closure of all non-essential retail outlets for an indefinite period. Government agencies are presently analysing how best to develop an exit strategy from these measures and to determine how the epidemic may progress once measures are lifted. Mathematical models are currently providing short and long term forecasts regarding the future course of the COVID-19 outbreak in the UK to support evidence-based policymaking. We present a deterministic, age-structured transmission model that uses real-time data on confirmed cases requiring hospital care and mortality to provide up-to-date predictions on epidemic spread in ten regions of the UK. The model captures a range of age-dependent heterogeneities, reduced transmission from asymptomatic infections and produces a good fit to the key epidemic features over time. We simulated a suite of scenarios to assess the impact of differing approaches to relaxing social distancing measures from 7th May 2020 on the estimated number of patients requiring inpatient and critical care treatment, and deaths. With regard to future epidemic outcomes, we investigated the impact of reducing compliance, ongoing shielding of elder age groups, reapplying stringent social distancing measures using region based triggers and the role of asymptomatic transmission. We find that significant relaxation of social distancing measures from 7th May onwards can lead to a rapid resurgence of COVID-19 disease and the health system being quickly overwhelmed by a sizeable, second epidemic wave. In all considered age-shielding based strategies, we projected serious demand on critical care resources during the course of the pandemic. The reintroduction and release of strict measures on a regional basis, based on ICU bed occupancy, results in a long epidemic tail, until the second half of 2021, but ensures that the health service is protected by reintroducing social distancing measures for all individuals in a region when required. Our work confirms the effectiveness of stringent non-pharmaceutical measures in March 2020 to suppress the epidemic. It also provides strong evidence to support the need for a cautious, measured approach to relaxation of lockdown measures, to protect the most vulnerable members of society and support the health service through subduing demand on hospital beds, in particular bed occupancy in intensive care units.