Unreported cases in the 2014-2016 Ebola epidemic: Spatiotemporal variation, and implications for estimating transmission

Global Incidence of Diarrheal Diseases-An Update Using an Interpretable Predictive Model Based on XGBoost and SHAP: A Systematic Analysis

BACKGROUND

Diarrheal disease remains a significant public health issue, particularly affecting young children and older adults. Despite efforts to control and prevent these diseases, their incidence continues to be a global concern. Understanding the trends in diarrhea incidence and the factors influencing these trends is crucial for developing effective public health strategies.

OBJECTIVE

This study aimed to explore the temporal trends in diarrhea incidence and associated factors from 1990 to 2019 and to project the incidence for the period 2020-2040 at global, regional, and national levels. We aimed to identify key factors influencing these trends to inform future prevention and control strategies.

METHODS

The eXtreme Gradient Boosting (XGBoost) model was used to predict the incidence from 2020 to 2040 based on demographic, meteorological, water sanitation, and sanitation and hygiene indicators. SHapley Additive exPlanations (SHAP) value was performed to explain the impact of variables in the model on the incidence. Estimated annual percentage change (EAPC) was calculated to assess the temporal trends of age-standardized incidence rates (ASIRs) from 1990 to 2019 and from 2020 to 2040.

RESULTS

Globally, both incident cases and ASIRs of diarrhea increased between 2010 and 2019. The incident cases are expected to rise from 2020 to 2040, while the ASIRs and incidence rates are predicted to slightly decrease. During the observed (1990-2019) and predicted (2020-2040) periods, adults aged 60 years and above exhibited an upward trend in incidence rate as age increased, while children aged < 5 years consistently had the highest incident cases. The SHAP framework was applied to explain the model predictions. We identified several risk factors associated with an increased incidence of diarrhea, including age over 60 years, yearly precipitation exceeding 3000 mm, temperature above 20 °C for both maximum and minimum values, and vapor pressure deficit over 1500 Pa. A decreased incidence rate was associated with relative humidity over 60%, wind speed over 4 m/s, and populations with above 80% using safely managed drinking water services and over 40% using safely managed sanitation services.

CONCLUSIONS

Diarrheal diseases are still serious public health concerns, with predicted increases in the incident cases despite decreasing ASIRs globally. Children aged < 5 years remain highly susceptible to diarrheal diseases, yet the incidence rate in the older adults aged 60 plus years still warrants additional attention. Additionally, more targeted efforts to improve access to safe drinking water and sanitation services are crucial for reducing the incidence of diarrheal diseases globally.

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.

Angular reproduction numbers improve estimates of transmissibility when disease generation times are misspecified or time-varying

We introduce the angular reproduction number Ω, which measures time-varying changes in epidemic transmissibility resulting from variations in both the effective reproduction number R, and generation time distribution w. Predominant approaches for tracking pathogen spread infer either R or the epidemic growth rate r. However, R is biased by mismatches between the assumed and true w, while r is difficult to interpret in terms of the individual-level branching process underpinning transmission. R and r may also disagree on the relative transmissibility of epidemics or variants (i.e. rA > rB does not imply RA > RB for variants A and B). We find that Ω responds meaningfully to mismatches and time-variations in w while mostly maintaining the interpretability of R. We prove that Ω > 1 implies R > 1 and that Ω agrees with r on the relative transmissibility of pathogens. Estimating Ω is no more difficult than inferring R, uses existing software, and requires no generation time measurements. These advantages come at the expense of selecting one free parameter. We propose Ω as complementary statistic to R and r that improves transmissibility estimates when w is misspecified or time-varying and better reflects the impact of interventions, when those interventions concurrently change R and w or alter the relative risk of co-circulating pathogens.

Using next generation matrices to estimate the proportion of infections that are not detected in an outbreak

Contact tracing, where exposed individuals are followed up to break ongoing transmission chains, is a key pillar of outbreak response for infectious disease outbreaks. Unfortunately, these systems are not fully effective, and infections can still go undetected as people may not remember all their contacts or contacts may not be traced successfully. A large proportion of undetected infections suggests poor contact tracing and surveillance systems, which could be a potential area of improvement for a disease response. In this paper, we present a method for estimating the proportion of infections that are not detected during an outbreak. Our method uses next generation matrices that are parameterized by linked contact tracing data and case line-lists. We validate the method using simulated data from an individual-based model and then investigate two case studies: the proportion of undetected infections in the SARS-CoV-2 outbreak in New Zealand during 2020 and the Ebola epidemic in Guinea during 2014. We estimate that only 5.26% of SARS-CoV-2 infections were not detected in New Zealand during 2020 (95% credible interval: 0.243 - 16.0%) if 80% of contacts were under active surveillance but depending on assumptions about the ratio of contacts not under active surveillance versus contacts under active surveillance 39.0% or 37.7% of Ebola infections were not detected in Guinea (95% credible intervals: 1.69 - 87.0% or 1.70 - 80.9%).

Guiding the design of SARS-CoV-2 genomic surveillance by estimating the resolution of outbreak detection

Genomic surveillance of SARS-CoV-2 has been essential to inform public health response to outbreaks. The high incidence of infection has resulted in a smaller proportion of cases undergoing whole genome sequencing due to finite resources. We present a framework for estimating the impact of reduced depths of genomic surveillance on the resolution of outbreaks, based on a clustering approach using pairwise genetic and temporal distances. We apply the framework to simulated outbreak data to show that outbreaks are detected less frequently when fewer cases are subjected to whole genome sequencing. The impact of sequencing fewer cases depends on the size of the outbreaks, and on the genetic and temporal similarity of the index cases of the outbreaks. We also apply the framework to an outbreak of the SARS-CoV-2 Delta variant in New South Wales, Australia. We find that the detection of clusters in the outbreak would have been delayed if fewer cases had been sequenced. Existing recommendations for genomic surveillance estimate the minimum number of cases to sequence in order to detect and monitor new virus variants, assuming representative sampling of cases. Our method instead measures the resolution of clustering, which is important for genomic epidemiology, and accommodates sampling biases.

Quantifying the information in noisy epidemic curves

Reliably estimating the dynamics of transmissible diseases from noisy surveillance data is an enduring problem in modern epidemiology. Key parameters are often inferred from incident time series, with the aim of informing policy-makers on the growth rate of outbreaks or testing hypotheses about the effectiveness of public health interventions. However, the reliability of these inferences depends critically on reporting errors and latencies innate to the time series. Here, we develop an analytical framework to quantify the uncertainty induced by under-reporting and delays in reporting infections, as well as a metric for ranking surveillance data informativeness. We apply this metric to two primary data sources for inferring the instantaneous reproduction number: epidemic case and death curves. We find that the assumption of death curves as more reliable, commonly made for acute infectious diseases such as COVID-19 and influenza, is not obvious and possibly untrue in many settings. Our framework clarifies and quantifies how actionable information about pathogen transmissibility is lost due to surveillance limitations.

Infectious Disease Underreporting Is Predicted by Country-Level Preparedness, Politics, and Pathogen Severity

Underreporting of infectious diseases is a pervasive challenge in public health that has emerged as a central issue in characterizing the dynamics of the COVID-19 pandemic. Infectious diseases are underreported for a range of reasons, including mild or asymptomatic infections, weak public health infrastructure, and government censorship. In this study, we investigated factors associated with cross-country and cross-pathogen variation in reporting. We performed a literature search to collect estimates of empirical reporting rates, calculated as the number of cases reported divided by the estimated number of true cases. This literature search yielded a dataset of reporting rates for 32 pathogens, representing 52 countries. We combined epidemiological and social science theory to identify factors specific to pathogens, country health systems, and politics that could influence empirical reporting rates. We performed generalized linear regression to test the relationship between the pathogen- and country-specific factors that we hypothesized could influence reporting rates, and the reporting rate estimates that we collected in our literature search. Pathogen- and country-specific factors were predictive of reporting rates. Deadlier pathogens and sexually transmitted diseases were more likely to be reported. Country epidemic preparedness was positively associated with reporting completeness, while countries with high levels of media bias in favor of incumbent governments were less likely to report infectious disease cases. Underreporting is a complex phenomenon that is driven by factors specific to pathogens, country health systems, and politics. In this study, we identified specific and measurable components of these broader factors that influence pathogen- and country-specific reporting rates and used model selection techniques to build a model that can guide efforts to diagnose, characterize, and reduce underreporting. Furthermore, this model can characterize uncertainty and correct for bias in reported infectious disease statistics, particularly when outbreak-specific empirical estimates of underreporting are unavailable. More precise estimates can inform control policies and improve the accuracy of infectious disease models.

Geospatial clustering and correlates of deaths during the Ebola outbreak in Liberia: a Bayesian geoadditive semiparametric analysis of nationally representative cross-sectional survey data

OBJECTIVE

To investigate the extent of geospatial clustering of reported deaths during the Ebola outbreak in Liberia and the covariates associated with the observed clustering.

DESIGN

Cross-sectional study.

PARTICIPANTS

Male and female respondents from the 2019-2020 Liberia Demographic and Health Survey. The analysis covered 11 928 (women=7854 and men=4074) respondents for whom complete data were available.

OUTCOME MEASURES

The outcome variable was the death of a household member or relative during the Ebola outbreak in Liberia, coded 1 if the respondent reported death and 0 otherwise.

METHODS

We applied the Bayesian geoadditive semiparametric regression to examine the extent of geospatial clustering of deaths at the district-level and community-level development and socioeconomic factors associated with the observed clustering.

RESULTS

Almost a quarter (24.8%) of all respondents reported the death of a household member or relative during the Ebola outbreak. The results show that deaths were clustered within districts in six (Grand Cape Mount, Bomi, Monsterrado, Margibi, Gbarpolu and Lofa) of the 15 counties in Liberia. Districts with high death clustering were all near or shared borders with Sierra Leone and Guinea. The community-level development indicators (global human footprint, gross cell production and population density) had a non-linear associative effect with the observed spatial clustering. Also, respondents' characteristics (respondent's age (non-linear effect), educational attainment and urban-rural place of residence) were associated with the observed clustering. The results show that death clustering during outbreaks was constrained to poor settings and impacts areas of moderate and high socioeconomic development.

CONCLUSION

Reported deaths during the Ebola outbreak in Liberia were not randomly distributed at the district level but clustered. The findings highlight the need to identify at-risk populations during epidemics and respond with the needed interventions to save lives.

Measuring the unknown: An estimator and simulation study for assessing case reporting during epidemics

The fraction of cases reported, known as 'reporting', is a key performance indicator in an outbreak response, and an essential factor to consider when modelling epidemics and assessing their impact on populations. Unfortunately, its estimation is inherently difficult, as it relates to the part of an epidemic which is, by definition, not observed. We introduce a simple statistical method for estimating reporting, initially developed for the response to Ebola in Eastern Democratic Republic of the Congo (DRC), 2018-2020. This approach uses transmission chain data typically gathered through case investigation and contact tracing, and uses the proportion of investigated cases with a known, reported infector as a proxy for reporting. Using simulated epidemics, we study how this method performs for different outbreak sizes and reporting levels. Results suggest that our method has low bias, reasonable precision, and despite sub-optimal coverage, usually provides estimates within close range (5-10%) of the true value. Being fast and simple, this method could be useful for estimating reporting in real-time in settings where person-to-person transmission is the main driver of the epidemic, and where case investigation is routinely performed as part of surveillance and contact tracing activities.

Mitigating bias in estimating epidemic severity due to heterogeneity of epidemic onset and data aggregation

Outbreaks of infectious diseases, such as influenza, are a major societal burden. Mitigation policies during an outbreak or pandemic are guided by the analysis of data of ongoing or preceding epidemics. The reproduction number, R0, defined as the expected number of secondary infections arising from a single individual in a population of susceptibles is critical to epidemiology. For typical compartmental models such as the Susceptible-Infected-Recovered (SIR) R0 represents the severity of an epidemic. It is an estimate of the early-stage growth rate of an epidemic and is an important threshold parameter used to gain insights into the spread or decay of an outbreak. Models typically use incidence counts as indicators of cases within a single large population; however, epidemic data are the result of a hierarchical aggregation, where incidence counts from spatially separated monitoring sites (or sub-regions) are pooled and used to infer R0. Is this aggregation approach valid when the epidemic has different dynamics across the regions monitored? We characterize bias in the estimation of R0 from a merged data set when the epidemics of the sub-regions, used in the merger, exhibit delays in onset. We propose a method to mitigate this bias, and study its efficacy on synthetic data as well as real-world influenza and COVID-19 data.

Risk Assessment of Importation and Local Transmission of COVID-19 in South Korea: Statistical Modeling Approach

Background

Despite recent achievements in vaccines, antiviral drugs, and medical infrastructure, the emergence of COVID-19 has posed a serious threat to humans worldwide. Most countries are well connected on a global scale, making it nearly impossible to implement perfect and prompt mitigation strategies for infectious disease outbreaks. In particular, due to the explosive growth of international travel, the complex network of human mobility enabled the rapid spread of COVID-19 globally.

Objective

South Korea was one of the earliest countries to be affected by COVID-19. In the absence of vaccines and treatments, South Korea has implemented and maintained stringent interventions, such as large-scale epidemiological investigations, rapid diagnosis, social distancing, and prompt clinical classification of severely ill patients with appropriate medical measures. In particular, South Korea has implemented effective airport screenings and quarantine measures. In this study, we aimed to assess the country-specific importation risk of COVID-19 and investigate its impact on the local transmission of COVID-19.

Methods

The country-specific importation risk of COVID-19 in South Korea was assessed. We investigated the relationships between country-specific imported cases, passenger numbers, and the severity of country-specific COVID-19 prevalence from January to October 2020. We assessed the country-specific risk by incorporating country-specific information. A renewal mathematical model was employed, considering both imported and local cases of COVID-19 in South Korea. Furthermore, we estimated the basic and effective reproduction numbers.

Results

The risk of importation from China was highest between January and February 2020, while that from North America (the United States and Canada) was high from April to October 2020. The R₀ was estimated at 1.87 (95% CI 1.47-2.34), using the rate of α=0.07 for secondary transmission caused by imported cases. The R_t was estimated in South Korea and in both Seoul and Gyeonggi.

Conclusions

A statistical model accounting for imported and locally transmitted cases was employed to estimate R₀ and R_t. Our results indicated that the prompt implementation of airport screening measures (contact tracing with case isolation and quarantine) successfully reduced local transmission caused by imported cases despite passengers arriving from high-risk countries throughout the year. Moreover, various mitigation interventions, including social distancing and travel restrictions within South Korea, have been effectively implemented to reduce the spread of local cases in South Korea.

The impact of the Ebola crisis on mortality and welfare in Liberia

This study assesses the impact of Ebola virus disease (EVD) outbreak on individual and total welfare in Liberia during 2014/15. By combining mortality and household consumption data, it estimates how much individuals would be hypothetically willing to pay to avoid the EVD-induced increase in age- and sex-specific mortality rates. The results suggest that the total welfare loss associated with EVD-related mortality ranges from $90 to $190 million, which is comparable to estimates based on the economic costs of EVD alone. In addition, the estimates lie between those derived from the cost-of-illness and value of statistical life approaches applied in previous works. This suggests that incorporating additional information on age- and sex-specific mortality, as well as individual consumption levels, provides a more accurate estimation of the welfare loss due to EVD-related mortality.

Epidemiological characteristics of and containment measures for COVID-19 in Busan, Korea

Objectives

To describe and evaluate epidemiological investigation results and containment measures implemented in Busan, where 108 cases were confirmed with coronavirus disease 2019 (COVID-19) between February 21, 2020 and March 24, 2020.

Methods

Any individual who tested positive for COVID-19 was classified as a confirmed case. Measures were taken to identify the source of infection and trace and quarantine contacts. Serial intervals were estimated and the effective reproduction number was computed.

Results

Of the total 18,303 COVID-19 tests performed between January 16, 2020 and March 24, 2020 in Busan, 108 yielded positive results (positive test rate, 0.6%). All confirmed cases were placed in isolation at hospitals. Of the 108 confirmed cases, 59 (54.6%) were female. The most common age group was 20-29 years with 37 cases (34.3%). Regarding symptoms at the time of diagnosis, cough (n=38, 35.2%) and fever (n=34, 31.5%) were most common; 12 cases (11.1%) were asymptomatic. The source of infection was identified in 99 cases (91.7%). A total of 3,223 contacts were identified and quarantined. Household contacts accounted for 196, and the household secondary attack rate was 8.2% (95% confidence interval [CI], 4.7 to 12.9). The mean serial interval was estimated to be 5.54 days (95% CI, 4.08 to 7.01). After February 26, (R_t) remained below 1 in Busan.

Conclusions

The early containment strategy implemented in Busan shows that control is possible if outbreaks are of limited scope. In preparation for future outbreaks, public health and healthcare systems should be re-examined and put in a ready state.

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

The World Health Organization considers an Ebola outbreak to have ended once 42 days have passed since the last possible exposure to a confirmed case. Benefits of a quick end-of-outbreak declaration, such as reductions in trade/travel restrictions, must be balanced against the chance of flare-ups from undetected residual cases. We show how epidemiological modelling can be used to estimate the surveillance level required for decision-makers to be confident that an outbreak is over. Results from a simple model characterizing an Ebola outbreak suggest that a surveillance sensitivity (i.e. case reporting percentage) of 79% is necessary for 95% confidence that an outbreak is over after 42 days without symptomatic cases. With weaker surveillance, unrecognized transmission may still occur: if the surveillance sensitivity is only 40%, then 62 days must be waited for 95% certainty. By quantifying the certainty in end-of-outbreak declarations, public health decision-makers can plan and communicate more effectively. This article is part of the theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control'. This issue is linked with the earlier theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes'.

A probabilistic census-travel model to predict introduction sites of exotic plant, animal and human pathogens

International travel offers an extensive network for new and recurring human-mediated introductions of exotic infectious pathogens and biota, freeing geographical constraints. We present a predictive census-travel model that integrates international travel with endpoint census data and epidemiological characteristics to predict points of introduction. Population demographics, inbound and outbound travel patterns, and quantification of source strength by country are combined to estimate and rank risk of introduction at user-scalable land parcel areas (e.g. state, county, zip code, census tract, gridded landscapes (1 mi², 5 km², etc.)). This risk ranking by parcel can be used to develop pathogen surveillance programmes, and has been incorporated in multiple US state/federal surveillance protocols. The census-travel model is versatile and independent of pathosystems, and applies a risk algorithm to generate risk maps for plant, human and animal contagions at different spatial scales. An interactive, user-friendly interface is available online (https://epi-models.shinyapps.io/Census_Travel/) to provide ease-of-use for regulatory agencies for early detection of high-risk exotics. The interface allows users to parametrize and run the model without knowledge of background code and underpinning data. 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'.

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.

Projections of epidemic transmission and estimation of vaccination impact during an ongoing Ebola virus disease outbreak in Northeastern Democratic Republic of Congo, as of Feb. 25, 2019

BACKGROUND

As of February 25, 2019, 875 cases of Ebola virus disease (EVD) were reported in North Kivu and Ituri Provinces, Democratic Republic of Congo. Since the beginning of October 2018, the outbreak has largely shifted into regions in which active armed conflict has occurred, and in which EVD cases and their contacts have been difficult for health workers to reach. We used available data on the current outbreak, with case-count time series from prior outbreaks, to project the short-term and long-term course of the outbreak.

METHODS

For short- and long-term projections, we modeled Ebola virus transmission using a stochastic branching process that assumes gradually quenching transmission rates estimated from past EVD outbreaks, with outbreak trajectories conditioned on agreement with the course of the current outbreak, and with multiple levels of vaccination coverage. We used two regression models to estimate similar projection periods. Short- and long-term projections were estimated using negative binomial autoregression and Theil-Sen regression, respectively. We also used Gott's rule to estimate a baseline minimum-information projection. We then constructed an ensemble of forecasts to be compared and recorded for future evaluation against final outcomes. From August 20, 2018 to February 25, 2019, short-term model projections were validated against known case counts.

RESULTS

During validation of short-term projections, from one week to four weeks, we found models consistently scored higher on shorter-term forecasts. Based on case counts as of February 25, the stochastic model projected a median case count of 933 cases by February 18 (95% prediction interval: 872-1054) and 955 cases by March 4 (95% prediction interval: 874-1105), while the auto-regression model projects median case counts of 889 (95% prediction interval: 876-933) and 898 (95% prediction interval: 877-983) cases for those dates, respectively. Projected median final counts range from 953 to 1,749. Although the outbreak is already larger than all past Ebola outbreaks other than the 2013-2016 outbreak of over 26,000 cases, our models do not project that it is likely to grow to that scale. The stochastic model estimates that vaccination coverage in this outbreak is lower than reported in its trial setting in Sierra Leone.

CONCLUSIONS

Our projections are concentrated in a range up to about 300 cases beyond those already reported. While a catastrophic outbreak is not projected, it is not ruled out, and prevention and vigilance are warranted. Prospective validation of our models in real time allowed us to generate more accurate short-term forecasts, and this process may prove useful for future real-time short-term forecasting. We estimate that transmission rates are higher than would be seen under target levels of 62% coverage due to contact tracing and vaccination, and this model estimate may offer a surrogate indicator for the outbreak response challenges.

Estimating undetected Ebola spillovers

The preparedness of health systems to detect, treat, and prevent onward transmission of Ebola virus disease (EVD) is central to mitigating future outbreaks. Early detection of outbreaks is critical to timely response, but estimating detection rates is difficult because unreported spillover events and outbreaks do not generate data. Using three independent datasets available on the distributions of secondary infections during EVD outbreaks across West Africa, in a single district (Western Area) of Sierra Leone, and in the city of Conakry, Guinea, we simulated realistic outbreak size distributions and compared them to reported outbreak sizes. These three empirical distributions lead to estimates for the proportion of detected spillover events and small outbreaks of 26% (range 8-40%, based on the full outbreak data), 48% (range 39-62%, based on the Sierra Leone data), and 17% (range 11-24%, based on the Guinea data). We conclude that at least half of all spillover events have failed to be reported since EVD was first recognized. We also estimate the probability of detecting outbreaks of different sizes, which is likely less than 10% for single-case spillover events. Comparing models of the observation process also suggests the probability of detecting an outbreak is not simply the cumulative probability of independently detecting any one individual. Rather, we find that any individual's probability of detection is highly dependent upon the size of the cluster of cases. These findings highlight the importance of primary health care and local case management to detect and contain undetected early stage outbreaks at source.

Projections of Ebola outbreak size and duration with and without vaccine use in Équateur, Democratic Republic of Congo, as of May 27, 2018

As of May 27, 2018, 6 suspected, 13 probable and 35 confirmed cases of Ebola virus disease (EVD) had been reported in Équateur Province, Democratic Republic of Congo. We used reported case counts and time series from prior outbreaks to estimate the total outbreak size and duration with and without vaccine use. We modeled Ebola virus transmission using a stochastic branching process model that included reproduction numbers from past Ebola outbreaks and a particle filtering method to generate a probabilistic projection of the outbreak size and duration conditioned on its reported trajectory to date; modeled using high (62%), low (44%), and zero (0%) estimates of vaccination coverage (after deployment). Additionally, we used the time series for 18 prior Ebola outbreaks from 1976 to 2016 to parameterize the Thiel-Sen regression model predicting the outbreak size from the number of observed cases from April 4 to May 27. We used these techniques on probable and confirmed case counts with and without inclusion of suspected cases. Probabilistic projections were scored against the actual outbreak size of 54 EVD cases, using a log-likelihood score. With the stochastic model, using high, low, and zero estimates of vaccination coverage, the median outbreak sizes for probable and confirmed cases were 82 cases (95% prediction interval [PI]: 55, 156), 104 cases (95% PI: 58, 271), and 213 cases (95% PI: 64, 1450), respectively. With the Thiel-Sen regression model, the median outbreak size was estimated to be 65.0 probable and confirmed cases (95% PI: 48.8, 119.7). Among our three mathematical models, the stochastic model with suspected cases and high vaccine coverage predicted total outbreak sizes closest to the true outcome. Relatively simple mathematical models updated in real time may inform outbreak response teams with projections of total outbreak size and duration.

Lessons from History

Resilience has a lengthy history of practice and implementation for events of extreme consequence and high uncertainty. One of the clearest cases of embryonic resilience thinking includes Medieval Venice, which was forced to grapple with the recurring threat of plague that threatened to destroy the fabric of European society and cripple the juggernaut of Venetian maritime trade (Linkov et al. 2014a, b, c, d, e; Lane 1973). This early resilience thinking did not fully inoculate Venetian society from the ravages of disease—on the contrary, limitations of medical knowledge and border control allowed for outbreaks throughout the early modern era—yet it did allow Venetian policymakers to begin to address the question of how to combat deadly disease. The cumulative successes in reducing disease incidence and spread throughout the city and its dependent settlements eventually brought policymakers to embrace resilience thinking for other unrelated projects ranging from climate change to land reclamation efforts—all centered on the idea of strengthening Venetian social, economic, and cultural capabilities in the midst of an uncertain future (Vergano and Nunes 2007; Linkov et al. 2014a, b, c, d, e). This all goes to show that while resilience thinking and resilience analysis are growing buzzwords in the early twenty-first century, their roots go back centuries before even the printing press or functional medicine.