Rigorous surveillance is necessary for high confidence in end-of-outbreak declarations for Ebola and other infectious diseases

Using real-time modelling to inform the 2017 Ebola outbreak response in DR Congo

Important policy questions during infections disease outbreaks include: i) How effective are particular interventions?; ii) When can resource-intensive interventions be removed? We used mathematical modelling to address these questions during the 2017 Ebola outbreak in Likati Health Zone, Democratic Republic of the Congo (DRC). Eight cases occurred before 15 May 2017, when the Ebola Response Team (ERT; co-ordinated by the World Health Organisation and DRC Ministry of Health) was deployed to reduce transmission. We used a branching process model to estimate that, pre-ERT arrival, the reproduction number was R = 1.49 (95% credible interval ( 0.67, 2.81 ) ). The risk of further cases occurring without the ERT was estimated to be 0.97 (97%). However, no cases materialised, suggesting that the ERT's measures were effective. We also estimated the risk of withdrawing the ERT in real-time. By the actual ERT withdrawal date (2 July 2017), the risk of future cases without the ERT was only 0.01, indicating that the ERT withdrawal decision was safe. We evaluated the sensitivity of our results to the estimated R value and considered different criteria for determining the ERT withdrawal date. This research provides an extensible modelling framework that can be used to guide decisions about when to relax interventions during future outbreaks.

Optimizing the timing of an end-of-outbreak declaration: Ebola virus disease in the Democratic Republic of the Congo

Following the apparent final case in an Ebola virus disease (EVD) outbreak, the decision to declare the outbreak over must balance societal benefits of relaxing interventions against the risk of resurgence. Estimates of the end-of-outbreak probability (the probability that no future cases will occur) provide quantitative evidence that can inform the timing of an end-of-outbreak declaration. An existing modeling approach for estimating the end-of-outbreak probability requires comprehensive contact tracing data describing who infected whom to be available, but such data are often unavailable or incomplete during outbreaks. Here, we develop a Markov chain Monte Carlo-based approach that extends the previous method and does not require contact tracing data. Considering data from two EVD outbreaks in the Democratic Republic of the Congo, we find that data describing who infected whom are not required to resolve uncertainty about when to declare an outbreak over.

A simulation-based approach for estimating the time-dependent reproduction number from temporally aggregated disease incidence time series data

Tracking pathogen transmissibility during infectious disease outbreaks is essential for assessing the effectiveness of public health measures and planning future control strategies. A key measure of transmissibility is the time-dependent reproduction number, which has been estimated in real-time during outbreaks of a range of pathogens from disease incidence time series data. While commonly used approaches for estimating the time-dependent reproduction number can be reliable when disease incidence is recorded frequently, such incidence data are often aggregated temporally (for example, numbers of cases may be reported weekly rather than daily). As we show, commonly used methods for estimating transmissibility can be unreliable when the timescale of transmission is shorter than the timescale of data recording. To address this, here we develop a simulation-based approach involving Approximate Bayesian Computation for estimating the time-dependent reproduction number from temporally aggregated disease incidence time series data. We first use a simulated dataset representative of a situation in which daily disease incidence data are unavailable and only weekly summary values are reported, demonstrating that our method provides accurate estimates of the time-dependent reproduction number under such circumstances. We then apply our method to two outbreak datasets consisting of weekly influenza case numbers in 2019-20 and 2022-23 in Wales (in the United Kingdom). Our simple-to-use approach will allow accurate estimates of time-dependent reproduction numbers to be obtained from temporally aggregated data during future infectious disease outbreaks.

Exact calculation of end-of-outbreak probabilities using contact tracing data

A key challenge for public health policymakers is determining when an infectious disease outbreak has finished. Following a period without cases, an estimate of the probability that no further cases will occur in future (the end-of-outbreak probability) can be used to inform whether or not to declare an outbreak over. An existing quantitative approach (the Nishiura method), based on a branching process transmission model, allows the end-of-outbreak probability to be approximated from disease incidence time series, the offspring distribution and the serial interval distribution. Here, we show how the end-of-outbreak probability under the same transmission model can be calculated exactly if data describing who-infected-whom (the transmission tree) are also available (e.g. from contact tracing studies). In that scenario, our novel approach (the traced transmission method) is straightforward to use. We demonstrate this by applying the method to data from previous outbreaks of Ebola virus disease and Nipah virus infection. For both outbreaks, the traced transmission method would have determined that the outbreak was over earlier than the Nishiura method. This highlights that collection of contact tracing data and application of the traced transmission method may allow stringent control interventions to be relaxed quickly at the end of an outbreak, with only a limited risk of outbreak resurgence.

Investigation of and Strategies to Control the Final Cluster of the 2018-2020 Ebola Virus Disease Outbreak in the Eastern Democratic Republic of Congo

Background

On April 10, 2020, while the independent committee of the International Health Regulation was meeting to decide whether the 10th Ebola outbreak in the Demogratic Republic of Congo still constituted a Public Health Emergency of International Concern, a new confirmed case was reported in the city of Beni, the last epicenter of the epidemic. This study aimed to understand the source of this cluster and learn from the implemented control strategies for improved response in the future.

Methods

We conducted a combined epidemiological and genomic investigation to understand the origins and dynamics of transmission within this cluster and describe the strategy that successfully controlled the outbreak.

Results

Eight cases were identified as belonging to this final cluster. A total of 1028 contacts were identified. Whole-genome sequencing revealed that all cases belonged to the same cluster, the closest sequence to which was identified as a case from the Beni area with symptom onset in July 2019 and a difference of just 31 nucleotides. Outbreak control measures included community confinement of high-risk contacts.

Conclusions

This study illustrates the high risk of additional flare-ups in the period leading to the end-of-outbreak declaration and the importance of maintaining enhanced surveillance and confinement activities to rapidly control Ebola outbreaks.

A quantitative method to project the probability of the end of an epidemic: Application to the COVID-19 outbreak in Wuhan, 2020

The end-of-outbreak declaration is an important part of epidemic control, marking the relaxation or cancellation of prevention and control measures. We propose a probability model to retrospectively quantify the confidence of giving the end-of-outbreak declaration during the COVID-19 epidemic in early 2020 in Wuhan. By using the linear spline, we firstly estimates the time-varying proportion of cases who miss the nonpharmaceutical interventions (NPIs) among all reported cases. Assuming the reproduction numbers being 1.5, 2.0, 3.0, 4.0, 5.0 and 6.0, the respective probability of the end of the COVID-19 outbreak with time after the last reported case can be iteratively computed. Consequently, the varying reproduction numbers produce slightly different increasing patterns of NPI effectiveness, and the end-of-outbreak declarations with 95% confidence are projected consistently earlier than the day when the lockdown was actually lifted. The reason for the timing discrepancy is discussed as well.

Assessment of Food and Waterborne Viral Outbreaks by Using Field Epidemiologic, Modern Laboratory and Statistical Methods-Lessons Learnt from Seven Major Norovirus Outbreaks in Finland

Seven major food- and waterborne norovirus outbreaks in Western Finland during 2014–2018 were re-analysed. The aim was to assess the effectiveness of outbreak investigation tools and evaluate the Kaplan criteria. We summarised epidemiological and microbiological findings from seven outbreaks. To evaluate the Kaplan criteria, a one-stage meta-analysis of data from seven cohort studies was performed. The case was defined as a person attending an implicated function with diarrhoea, vomiting or two other symptoms. Altogether, 22% (386/1794) of persons met the case definition. Overall adjusted, 73% of norovirus patients were vomiting, the mean incubation period was 44 h (4 h to 4 days) and the median duration of illness was 46 h. As vomiting was a more common symptom in children (96%, 143/149) and diarrhoea among the elderly (92%, 24/26), symptom and age presentation should drive hypothesis formulation. The Kaplan criteria were useful in initial outbreak assessments prior to faecal results. Rapid food control inspections enabled evidence-based, public-health-driven risk assessments. This led to probability-based vehicle identification and aided in resolving the outbreak event mechanism rather than implementing potentially ineffective, large-scale public health actions such as the withdrawal of extensive food lots. Asymptomatic food handlers should be ideally withdrawn from high-risk work for five days instead of the current two days. Food and environmental samples often remain negative with norovirus, highlighting the importance of research collaborations. Electronic questionnaire and open-source novel statistical programmes provided time and resource savings. The public health approach proved useful within the environmental health area with shoe leather field epidemiology, combined with statistical analysis and mathematical reasoning.

A hospital-related outbreak of SARS-CoV-2 associated with variant Epsilon (B.1.429) in Taiwan: transmission potential and outbreak containment under intensified contact tracing, January-February 2021

OBJECTIVES

A hospital-related cluster of 22 cases of coronavirus disease 2019 (COVID-19) occurred in Taiwan in January-February 2021. Rigorous control measures were introduced and could only be relaxed once the outbreak was declared over. Each day after the apparent outbreak end, we estimated the risk of future cases occurring in order to inform decision-making.

METHODS

Probabilistic transmission networks were reconstructed, and transmission parameters (the reproduction number R and overdispersion parameter k) were estimated. The reporting delay during the outbreak was estimated (Scenario 1). In addition, a counterfactual scenario with less effective interventions characterized by a longer reporting delay was considered (Scenario 2). Each day, the risk of future cases was estimated under both scenarios.

RESULTS

The values of R and k were estimated to be 1.30 ((95% credible interval (CI) 0.57-3.80) and 0.38 (95% CI 0.12-1.20), respectively. The mean reporting delays considered were 2.5 days (Scenario 1) and 7.8 days (Scenario 2). Following the final case, ttthe inferred probability of future cases occurring declined more quickly in Scenario 1 than Scenario 2.

CONCLUSIONS

Rigorous control measures allowed the outbreak to be declared over quickly following outbreak containment. This highlights the need for effective interventions, not only to reduce cases during outbreaks but also to allow outbreaks to be declared over with confidence.

A Quantitative Framework for Defining the End of an Infectious Disease Outbreak: Application to Ebola Virus Disease

The end-of-outbreak declaration is an important step in controlling infectious disease outbreaks. Objective estimation of the confidence level that an outbreak is over is important to reduce the risk of postdeclaration flare-ups. We developed a simulation-based model with which to quantify that confidence and tested it on simulated Ebola virus disease data. We found that these confidence estimates were most sensitive to the instantaneous reproduction number, the reporting rate, and the time between the symptom onset and death or recovery of the last detected case. For Ebola virus disease, our results suggested that the current World Health Organization criterion of 42 days since the recovery or death of the last detected case is too short and too sensitive to underreporting. Therefore, we suggest a shift to a preliminary end-of-outbreak declaration after 63 days from the symptom onset day of the last detected case. This preliminary declaration should still be followed by 90 days of enhanced surveillance to capture potential flare-ups of cases, after which the official end of the outbreak can be declared. This sequence corresponds to more than 95% confidence that an outbreak is over in most of the scenarios examined. Our framework is generic and therefore could be adapted to estimate end-of-outbreak confidence for other infectious diseases.

Epidemiological, clinical, and public health response characteristics of a large outbreak of diphtheria among the Rohingya population in Cox's Bazar, Bangladesh, 2017 to 2019: A retrospective study

BACKGROUND

Unrest in Myanmar in August 2017 resulted in the movement of over 700,000 Rohingya refugees to overcrowded camps in Cox's Bazar, Bangladesh. A large outbreak of diphtheria subsequently began in this population.

METHODS AND FINDINGS

Data were collected during mass vaccination campaigns (MVCs), contact tracing activities, and from 9 Diphtheria Treatment Centers (DTCs) operated by national and international organizations. These data were used to describe the epidemiological and clinical features and the control measures to prevent transmission, during the first 2 years of the outbreak. Between November 10, 2017 and November 9, 2019, 7,064 cases were reported: 285 (4.0%) laboratory-confirmed, 3,610 (51.1%) probable, and 3,169 (44.9%) suspected cases. The crude attack rate was 51.5 cases per 10,000 person-years, and epidemic doubling time was 4.4 days (95% confidence interval [CI] 4.2-4.7) during the exponential growth phase. The median age was 10 years (range 0-85), and 3,126 (44.3%) were male. The typical symptoms were sore throat (93.5%), fever (86.0%), pseudomembrane (34.7%), and gross cervical lymphadenopathy (GCL; 30.6%). Diphtheria antitoxin (DAT) was administered to 1,062 (89.0%) out of 1,193 eligible patients, with adverse reactions following among 229 (21.6%). There were 45 deaths (case fatality ratio [CFR] 0.6%). Household contacts for 5,702 (80.7%) of 7,064 cases were successfully traced. A total of 41,452 contacts were identified, of whom 40,364 (97.4%) consented to begin chemoprophylaxis; adherence was 55.0% (N = 22,218) at 3-day follow-up. Unvaccinated household contacts were vaccinated with 3 doses (with 4-week interval), while a booster dose was administered if the primary vaccination schedule had been completed. The proportion of contacts vaccinated was 64.7% overall. Three MVC rounds were conducted, with administrative coverage varying between 88.5% and 110.4%. Pentavalent vaccine was administered to those aged 6 weeks to 6 years, while tetanus and diphtheria (Td) vaccine was administered to those aged 7 years and older. Lack of adequate diagnostic capacity to confirm cases was the main limitation, with a majority of cases unconfirmed and the proportion of true diphtheria cases unknown.

CONCLUSIONS

To our knowledge, this is the largest reported diphtheria outbreak in refugee settings. We observed that high population density, poor living conditions, and fast growth rate were associated with explosive expansion of the outbreak during the initial exponential growth phase. Three rounds of mass vaccinations targeting those aged 6 weeks to 14 years were associated with only modestly reduced transmission, and additional public health measures were necessary to end the outbreak. This outbreak has a long-lasting tail, with Rt oscillating at around 1 for an extended period. An adequate global DAT stockpile needs to be maintained. All populations must have access to health services and routine vaccination, and this access must be maintained during humanitarian crises.

Localized end-of-outbreak determination for coronavirus disease 2019 (COVID-19): examples from clusters in Japan

OBJECTIVES

End-of-outbreak declarations are an important component of outbreak response because they indicate that public health and social interventions may be relaxed or lapsed. Our study aimed to assess end-of-outbreak probabilities for clusters of coronavirus disease 2019 (COVID-19) cases detected during the first wave of the COVID-19 pandemic in Japan.

METHODS

A statistical model for end-of-outbreak determination, which accounted for reporting delays for new cases, was computed. Four clusters, representing different social contexts and time points during the first wave of the epidemic, were selected and their end-of-outbreak probabilities were evaluated.

RESULTS

The speed of end-of-outbreak determination was most closely tied to outbreak size. Notably, accounting underascertainment of cases led to later end-of-outbreak determinations. In addition, end-of-outbreak determination was closely related to estimates of case dispersionk and the effective reproduction number Re. Increasing local transmission (Re>1) leads to greater uncertainty in the probability estimates.

CONCLUSIONS

When public health measures are effective, lowerRe (less transmission on average) and larger k (lower risk of superspreading) will be in effect, and end-of-outbreak determinations can be declared with greater confidence. The application of end-of-outbreak probabilities can help distinguish between local extinction and low levels of transmission, and communicating these end-of-outbreak probabilities can help inform public health decision making with regard to the appropriate use of resources.

How epidemics end

As COVID-19 drags on and new vaccines promise widespread immunity, the world's attention has turned to predicting how the present pandemic will end. How do societies know when an epidemic is over and normal life can resume? What criteria and markers indicate such an end? Who has the insight, authority, and credibility to decipher these signs? Detailed research on past epidemics has demonstrated that they do not end suddenly; indeed, only rarely do the diseases in question actually end. This article examines the ways in which scholars have identified and described the end stages of previous epidemics, pointing out that significantly less attention has been paid to these periods than to origins and climaxes. Analysis of the ends of epidemics illustrates that epidemics are as much social, political, and economic events as they are biological; the "end," therefore, is as much a process of social and political negotiation as it is biomedical. Equally important, epidemics end at different times for different groups, both within one society and across regions. Multidisciplinary research into how epidemics end reveals how the end of an epidemic shifts according to perspective, whether temporal, geographic, or methodological. A multidisciplinary analysis of how epidemics end suggests that epidemics should therefore be framed not as linear narratives-from outbreak to intervention to termination-but within cycles of disease and with a multiplicity of endings.

Predicting the number of reported and unreported cases for the COVID-19 epidemics in China, South Korea, Italy, France, Germany and United Kingdom

We model the COVID-19 coronavirus epidemics in China, South Korea, Italy, France, Germany and the United Kingdom. We identify the early phase of the epidemics, when the number of cases grows exponentially, before government implementation of major control measures. We identify the next phase of the epidemics, when these social measures result in a time-dependent exponentially decreasing number of cases. We use reported case data, both asymptomatic and symptomatic, to model the transmission dynamics. We also incorporate into the transmission dynamics unreported cases. We construct our models with comprehensive consideration of the identification of model parameters. A key feature of our model is the evaluation of the timing and magnitude of implementation of major public policies restricting social movement. We project forward in time the development of the epidemics in these countries based on our model analysis.

[Epidemiology of Viral Hemorrhagic Fever in Africa]

A variety of viral hemorrhagic fevers such as Ebola virus disease exist in Africa and impose a great threat in public health due to their high fatality. It is considered to be difficult to eradicate the etiological agents of viral hemorrhagic fever because they have non-human natural hosts. Therefore, the importance of public health measures remains high in addition to the urgent need for the development of medicines for treatment and prevention. Furthermore, public health measures directly lead to the accumulation of epidemiological knowledge about the diseases. As an infectious disease consultant for the World Health Organization, I have been involved with public health activities including the development of clinical guidelines, the establishment of laboratory diagnostic systems, the training for infection, prevention and control, the planning of budget for outbreak response, and the analysis of epidemiological data. On the last point, I reported the situation of Ebola virus disease outbreak in Liberia, 2014-2015 and Lassa fever outbreak in Nigeria, 2018-2019 describing the risk factors, morbidity, and mortality of the diseases.

An exact method for quantifying the reliability of end-of-epidemic declarations in real time

We derive and validate a novel and analytic method for estimating the probability that an epidemic has been eliminated (i.e. that no future local cases will emerge) in real time. When this probability crosses 0.95 an outbreak can be declared over with 95% confidence. Our method is easy to compute, only requires knowledge of the incidence curve and the serial interval distribution, and evaluates the statistical lifetime of the outbreak of interest. Using this approach, we show how the time-varying under-reporting of infected cases will artificially inflate the inferred probability of elimination, leading to premature (false-positive) end-of-epidemic declarations. Contrastingly, we prove that incorrectly identifying imported cases as local will deceptively decrease this probability, resulting in delayed (false-negative) declarations. Failing to sustain intensive surveillance during the later phases of an epidemic can therefore substantially mislead policymakers on when it is safe to remove travel bans or relax quarantine and social distancing advisories. World Health Organisation guidelines recommend fixed (though disease-specific) waiting times for end-of-epidemic declarations that cannot accommodate these variations. Consequently, there is an unequivocal need for more active and specialised metrics for reliably identifying the conclusion of an epidemic.

Will an outbreak exceed available resources for control? Estimating the risk from invading pathogens using practical definitions of a severe epidemic

Forecasting whether or not initial reports of disease will be followed by a severe epidemic is an important component of disease management. Standard epidemic risk estimates involve assuming that infections occur according to a branching process and correspond to the probability that the outbreak persists beyond the initial stochastic phase. However, an alternative assessment is to predict whether or not initial cases will lead to a severe epidemic in which available control resources are exceeded. We show how this risk can be estimated by considering three practically relevant potential definitions of a severe epidemic; namely, an outbreak in which: (i) a large number of hosts are infected simultaneously; (ii) a large total number of infections occur; and (iii) the pathogen remains in the population for a long period. We show that the probability of a severe epidemic under these definitions often coincides with the standard branching process estimate for the major epidemic probability. However, these practically relevant risk assessments can also be different from the major epidemic probability, as well as from each other. This holds in different epidemiological systems, highlighting that careful consideration of how to classify a severe epidemic is vital for accurate epidemic risk quantification.

Key questions for modelling COVID-19 exit strategies

Combinations of intense non-pharmaceutical interventions (lockdowns) were introduced worldwide to reduce SARS-CoV-2 transmission. Many governments have begun to implement exit strategies that relax restrictions while attempting to control the risk of a surge in cases. Mathematical modelling has played a central role in guiding interventions, but the challenge of designing optimal exit strategies in the face of ongoing transmission is unprecedented. Here, we report discussions from the Isaac Newton Institute 'Models for an exit strategy' workshop (11-15 May 2020). A diverse community of modellers who are providing evidence to governments worldwide were asked to identify the main questions that, if answered, would allow for more accurate predictions of the effects of different exit strategies. Based on these questions, we propose a roadmap to facilitate the development of reliable models to guide exit strategies. This roadmap requires a global collaborative effort from the scientific community and policymakers, and has three parts: (i) improve estimation of key epidemiological parameters; (ii) understand sources of heterogeneity in populations; and (iii) focus on requirements for data collection, particularly in low-to-middle-income countries. This will provide important information for planning exit strategies that balance socio-economic benefits with public health.

On a Coupled Time-Dependent SIR Models Fitting with New York and New-Jersey States COVID-19 Data

This article describes a simple Susceptible Infected Recovered (SIR) model fitting with COVID-19 data for the month of March 2020 in New York (NY) state. The model is a classical SIR, but is non-autonomous; the rate of susceptible people becoming infected is adjusted over time in order to fit the available data. The death rate is also secondarily adjusted. Our fitting is made under the assumption that due to limiting number of tests, a large part of the infected population has not been tested positive. In the last part, we extend the model to take into account the daily fluxes between New Jersey (NJ) and NY states and fit the data for both states. Our simple model fits the available data, and illustrates typical dynamics of the disease: exponential increase, apex and decrease. The model highlights a decrease in the transmission rate over the period which gives a quantitative illustration about how lockdown policies reduce the spread of the pandemic. The coupled model with NY and NJ states shows a wave in NJ following the NY wave, illustrating the mechanism of spread from one attractive hot spot to its neighbor.

Preface to theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control'

This preface forms part of the theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control'. This theme issue is linked with the earlier issue 'Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes'.

Translating surveillance data into incidence estimates

Monitoring a population for a disease requires the hosts to be sampled and tested for the pathogen. This results in sampling series from which we may estimate the disease incidence, i.e. the proportion of hosts infected. Existing estimation methods assume that disease incidence does not change between monitoring rounds, resulting in an underestimation of the disease incidence. In this paper, we develop an incidence estimation model accounting for epidemic growth with monitoring rounds that sample varying incidence. We also show how to accommodate the asymptomatic period that is the characteristic of most diseases. For practical use, we produce an approximation of the model, which is subsequently shown to be accurate for relevant epidemic and sampling parameters. Both the approximation and the full model are applied to stochastic spatial simulations of epidemics. The results prove their consistency for a very wide range of situations. The estimation model is made available as an online application. This article is part of the theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control'. This theme issue is linked with the earlier issue 'Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes'.

How decision makers can use quantitative approaches to guide outbreak responses

Decision makers are responsible for directing staffing, logistics, selecting public health interventions, communicating to professionals and the public, planning future response needs, and establishing strategic and tactical priorities along with their funding requirements. Decision makers need to rapidly synthesize data from different experts across multiple disciplines, bridge data gaps and translate epidemiological analysis into an operational set of decisions for disease control. Analytic approaches can be defined for specific response phases: investigation, scale-up and control. These approaches include: improved applications of quantitative methods to generate insightful epidemiological descriptions of outbreaks; robust investigations of causal agents and risk factors; tools to assess response needs; identifying and monitoring optimal interventions or combinations of interventions; and forecasting for response planning. Data science and quantitative approaches can improve decision-making in outbreak response. To realize these benefits, we need to develop a structured approach that will improve the quality and timeliness of data collected during outbreaks, establish analytic teams within the response structure and define a research agenda for data analytics in outbreak response.

This article is part of the theme issue ‘Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control’. This theme issue is linked with the earlier issue ‘Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes’.

Detection, forecasting and control of infectious disease epidemics: modelling outbreaks in humans, animals and plants

The 1918 influenza pandemic is one of the most devastating infectious disease epidemics on record, having caused approximately 50 million deaths worldwide. Control measures, including prohibiting non-essential gatherings as well as closing cinemas and music halls, were applied with varying success and limited knowledge of transmission dynamics. One hundred years later, following developments in the field of mathematical epidemiology, models are increasingly used to guide decision-making and devise appropriate interventions that mitigate the impacts of epidemics. Epidemiological models have been used as decision-making tools during outbreaks in human, animal and plant populations. However, as the subject has developed, human, animal and plant disease modelling have diverged. Approaches have been developed independently for pathogens of each host type, often despite similarities between the models used in these complementary fields. With the increased importance of a One Health approach that unifies human, animal and plant health, we argue that more inter-disciplinary collaboration would enhance each of the related disciplines. This pair of theme issues presents research articles written by human, animal and plant disease modellers. In this introductory article, we compare the questions pertinent to, and approaches used by, epidemiological modellers of human, animal and plant pathogens, and summarize the articles in these theme issues. We encourage future collaboration that transcends disciplinary boundaries and links the closely related areas of human, animal and plant disease epidemic modelling. This article is part of the theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes'. This issue is linked with the subsequent theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control'.

Improved inference of time-varying reproduction numbers during infectious disease outbreaks

Accurate estimation of the parameters characterising infectious disease transmission is vital for optimising control interventions during epidemics. A valuable metric for assessing the current threat posed by an outbreak is the time-dependent reproduction number, i.e. the expected number of secondary cases caused by each infected individual. This quantity can be estimated using data on the numbers of observed new cases at successive times during an epidemic and the distribution of the serial interval (the time between symptomatic cases in a transmission chain). Some methods for estimating the reproduction number rely on pre-existing estimates of the serial interval distribution and assume that the entire outbreak is driven by local transmission. Here we show that accurate inference of current transmissibility, and the uncertainty associated with this estimate, requires: (i) up-to-date observations of the serial interval to be included, and; (ii) cases arising from local transmission to be distinguished from those imported from elsewhere. We demonstrate how pathogen transmissibility can be inferred appropriately using datasets from outbreaks of H1N1 influenza, Ebola virus disease and Middle-East Respiratory Syndrome. We present a tool for estimating the reproduction number in real-time during infectious disease outbreaks accurately, which is available as an R software package (EpiEstim 2.2). It is also accessible as an interactive, user-friendly online interface (EpiEstim App), permitting its use by non-specialists. Our tool is easy to apply for assessing the transmission potential, and hence informing control, during future outbreaks of a wide range of invading pathogens.

Improved inference of time-varying reproduction numbers during infectious disease outbreaks

Accurate estimation of the parameters characterising infectious disease transmission is vital for optimising control interventions during epidemics. A valuable metric for assessing the current threat posed by an outbreak is the time-dependent reproduction number, i.e. the expected number of secondary cases caused by each infected individual. This quantity can be estimated using data on the numbers of observed new cases at successive times during an epidemic and the distribution of the serial interval (the time between symptomatic cases in a transmission chain). Some methods for estimating the reproduction number rely on pre-existing estimates of the serial interval distribution and assume that the entire outbreak is driven by local transmission. Here we show that accurate inference of current transmissibility, and the uncertainty associated with this estimate, requires: (i) up-to-date observations of the serial interval to be included, and; (ii) cases arising from local transmission to be distinguished from those imported from elsewhere. We demonstrate how pathogen transmissibility can be inferred appropriately using datasets from outbreaks of H1N1 influenza, Ebola virus disease and Middle-East Respiratory Syndrome. We present a tool for estimating the reproduction number in real-time during infectious disease outbreaks accurately, which is available as an R software package (EpiEstim 2.2). It is also accessible as an interactive, user-friendly online interface (EpiEstim App), permitting its use by non-specialists. Our tool is easy to apply for assessing the transmission potential, and hence informing control, during future outbreaks of a wide range of invading pathogens.

Accurate forecasts of the effectiveness of interventions against Ebola may require models that account for variations in symptoms during infection

Epidemiological models are routinely used to predict the effects of interventions aimed at reducing the impacts of Ebola epidemics. Most models of interventions targeting symptomatic hosts, such as isolation or treatment, assume that all symptomatic hosts are equally likely to be detected. In other words, following an incubation period, the level of symptoms displayed by an individual host is assumed to remain constant throughout an infection. In reality, however, symptoms vary between different stages of infection. During an Ebola infection, individuals progress from initial non-specific symptoms through to more severe phases of infection. Here we compare predictions of a model in which a constant symptoms level is assumed to those generated by a more epidemiologically realistic model that accounts for varying symptoms during infection. Both models can reproduce observed epidemic data, as we show by fitting the models to data from the ongoing epidemic in the Democratic Republic of the Congo and the 2014-16 epidemic in Liberia. However, for both of these epidemics, when interventions are altered identically in the models with and without levels of symptoms that depend on the time since first infection, predictions from the models differ. Our work highlights the need to consider whether or not varying symptoms should be accounted for in models used by decision makers to assess the likely efficacy of Ebola interventions.