A systematic review of early modelling studies of Ebola virus disease in West Africa

Ebola virus disease mathematical models and epidemiological parameters: a systematic review

Ebola virus disease poses a recurring risk to human health. We conducted a systematic review (PROSPERO CRD42023393345) of Ebola virus disease transmission models and parameters published from database inception to July 7, 2023, from PubMed and Web of Science. Two people screened each abstract and full text. Papers were extracted with a bespoke Access database, 10% were double extracted. We extracted 1280 parameters and 295 models from 522 papers. Basic reproduction number estimates were highly variable, as were effective reproduction numbers, likely reflecting spatiotemporal variability in interventions. Random-effect estimates were 15·4 days (95% CI 13·2-17·5) for the serial interval, 8·5 days (7·7-9·2) for the incubation period, 9·3 days (8·5-10·1) for the symptom-onset-to-death delay, and 13·0 days (10·4-15·7) for symptom-onset-to-recovery. Common effect estimates were similar, albeit with narrower CIs. Case-fatality ratio estimates were generally high but highly variable, which could reflect heterogeneity in underlying risk factors. Although a substantial body of literature exists on Ebola virus disease models and epidemiological parameter estimates, many of these studies focus on the west African Ebola epidemic and are primarily associated with Zaire Ebola virus, which leaves a key gap in our knowledge regarding other Ebola virus species and outbreak contexts.

The probability of epidemic burnout in the stochastic SIR model with vital dynamics

We present an approach to computing the probability of epidemic "burnout," i.e., the probability that a newly emergent pathogen will go extinct after a major epidemic. Our analysis is based on the standard stochastic formulation of the Susceptible-Infectious-Removed (SIR) epidemic model including host demography (births and deaths) and corresponds to the standard SIR ordinary differential equations (ODEs) in the infinite population limit. Exploiting a boundary layer approximation to the ODEs and a birth-death process approximation to the stochastic dynamics within the boundary layer, we derive convenient, fully analytical approximations for the burnout probability. We demonstrate-by comparing with computationally demanding individual-based stochastic simulations and with semi-analytical approximations derived previously-that our fully analytical approximations are highly accurate for biologically plausible parameters. We show that the probability of burnout always decreases with increased mean infectious period. However, for typical biological parameters, there is a relevant local minimum in the probability of persistence as a function of the basic reproduction number [Formula: see text]. For the shortest infectious periods, persistence is least likely if [Formula: see text]; for longer infectious periods, the minimum point decreases to [Formula: see text]. For typical acute immunizing infections in human populations of realistic size, our analysis of the SIR model shows that burnout is almost certain in a well-mixed population, implying that susceptible recruitment through births is insufficient on its own to explain disease persistence.

The basic reproduction number (R0) of ebola virus disease: A systematic review and meta-analysis

BACKGROUND

Ebola virus disease (Ebola) is highly pathogenic, transmissible, and often deadly, with debilitating consequences. Superspreading within a cluster is also possible. In this study, we aim to document Ebola basic reproduction number (R0): the average number of new cases associated with an Ebola case in a completely susceptible population.

METHODS

We undertook a systematic review and meta-analysis. We searched PubMed, EMBASE, and Web of Science for studies published between 1976 and February 27, 2023. We also manually searched the reference lists of the reviewed studies to identify additional studies. We included studies that reported R0 during Ebola outbreaks in Africa. We excluded studies that reported only the effective reproduction number (Rt). Abstracting data from included studies was performed using a pilot-tested standard form. Two investigators reviewed the studies, extracted the data, and assessed quality. The pooled R0 was determined by a random-effects meta-analysis. R0 was stratified by country. We also estimated the theoretically required immunization coverage to reach herd-immunity using the formula of (1-1/R0) × 100 %.

RESULTS

The search yielded 2042 studies. We included 53 studies from six African countries in the systematic review providing 97 Ebola mean R0 estimates. 27 (with 46 data points) studies were included in the meta-analysis. The overall pooled mean Ebola R0 was 1.95 (95 % CI 1.74-2.15), with high heterogeneity (I2 = 99.99 %; τ2 = 0.38; and p < 0.001) and evidence of small-study effects (Egger's statistics: Z = 4.67; p < 0.001). Mean Ebola R0 values ranged from 1.2 to 10.0 in Nigeria, 1.1 to 7 in Guinea, 1.14 to 8.33 in Sierra Leone, 1.13 to 5 in Liberia, 1.2 to 5.2 in DR Congo, 1.34 to 2.7 in Uganda, and from 1.40 to 2.55 for all West African countries combined. Pooled mean Ebola R0 was 9.38 (95 % CI 4.16-14.59) in Nigeria, 3.31 (95 % CI 2.30-4.32) in DR Congo, 2.0 (95 % CI 1.25-2.76) in Uganda, 1.83 (95 % CI 1.61-2.05) in Liberia, 1.73 (95 % CI 1.47-2.0) in Sierra Leonne, and 1.44 (95 % CI 1.29-1.60) in Guinea. In theory, 50 % of the population needs to be vaccinated to achieve herd immunity, assuming that Ebola vaccine would be 100 % effective.

CONCLUSIONS

Ebola R0 varies widely across countries. Ebola has a much wider R0 range than is often claimed (1.3-2.0). It is possible for an Ebola index case to infect more than two susceptible individuals.

Fundamental bound on epidemic overshoot in the SIR model

We derive an exact upper bound on the epidemic overshoot for the Kermack-McKendrick SIR model. This maximal overshoot value of 0.2984 · · · occurs at [Formula: see text]. In considering the utility of the notion of overshoot, a rudimentary analysis of data from the first wave of the COVID-19 pandemic in Manaus, Brazil highlights the public health hazard posed by overshoot for epidemics with R0 near 2. Using the general analysis framework presented within, we then consider more complex SIR models that incorporate vaccination.

Quantitatively assessing early detection strategies for mitigating COVID-19 and future pandemics

Researchers and policymakers have proposed systems to detect novel pathogens earlier than existing surveillance systems by monitoring samples from hospital patients, wastewater, and air travel, in order to mitigate future pandemics. How much benefit would such systems offer? We developed, empirically validated, and mathematically characterized a quantitative model that simulates disease spread and detection time for any given disease and detection system. We find that hospital monitoring could have detected COVID-19 in Wuhan 0.4 weeks earlier than it was actually discovered, at 2,300 cases (standard error: 76 cases) compared to 3,400 (standard error: 161 cases). Wastewater monitoring would not have accelerated COVID-19 detection in Wuhan, but provides benefit in smaller catchments and for asymptomatic or long-incubation diseases like polio or HIV/AIDS. Monitoring of air travel provides little benefit in most scenarios we evaluated. In sum, early detection systems can substantially mitigate some future pandemics, but would not have changed the course of COVID-19.

Estimation of a Within-Herd Transmission Rate for African Swine Fever in Vietnam

We describe results from a panel study in which pigs from a 17-sow African swine fever (ASF) positive herd in Thái Bình province, Vietnam, were followed over time to record the date of onset of ASF signs and the date of death from ASF. Our objectives were to (1) fit a susceptible-exposed-infectious-removed disease model to the data with transmission coefficients estimated using approximate Bayesian computation; (2) provide commentary on how a model of this type might be used to provide decision support for disease control authorities. For the outbreak in this herd, the median of the average latent period was 10 days (95% HPD (highest posterior density interval): 2 to 19 days), and the median of the average duration of infectiousness was 3 days (95% HPD: 2 to 4 days). The estimated median for the transmission coefficient was 3.3 (95% HPD: 0.4 to 8.9) infectious contacts per ASF-infectious pig per day. The estimated median for the basic reproductive number, R₀, was 10 (95% HPD: 1.1 to 30). Our estimates of the basic reproductive number R₀ were greater than estimates of R₀ for ASF reported previously. The results presented in this study may be used to estimate the number of pigs expected to be showing clinical signs at a given number of days following an estimated incursion date. This will allow sample size calculations, with or without adjustment to account for less than perfect sensitivity of clinical examination, to be used to determine the appropriate number of pigs to examine to detect at least one with the disease. A second use of the results of this study would be to inform the equation-based within-herd spread components of stochastic agent-based and hybrid simulation models of ASF.

A drug-disease model for predicting survival in an Ebola outbreak

REGN-EB3 (Inmazeb) is a cocktail of three human monoclonal antibodies approved for treatment of Ebola infection. This paper describes development of a mathematical model linking REGN-EB3's inhibition of Ebola virus to survival in a non-human primate (NHP) model, and translational scaling to predict survival in humans. Pharmacokinetic/pharmacodynamic data from single- and multiple-dose REGN-EB3 studies in infected rhesus macaques were incorporated. Using discrete indirect response models, the antiviral mechanism of action was used as a forcing function to drive the reversal of key Ebola disease hallmarks over time, for example, liver and kidney damage (elevated alanine [ALT] and aspartate aminotransferases [AST], blood urea nitrogen [BUN], and creatinine), and hemorrhage (decreased platelet count). A composite disease characteristic function was introduced to describe disease severity and integrated with the ordinary differential equations estimating the time course of clinical biomarkers. Model simulation results appropriately represented the concentration-dependence of the magnitude and time course of Ebola infection (viral and pathophysiological), including time course of viral load, ALT and AST elevations, platelet count, creatinine, and BUN. The model estimated the observed survival rate in rhesus macaques and the dose of REGN-EB3 required for saturation of the pharmacodynamic effects of viral inhibition, reversal of Ebola pathophysiology, and survival. The model also predicted survival in clinical trials with appropriate scaling to humans. This mathematical investigation demonstrates that drug-disease modeling can be an important translational tool to integrate preclinical data from an NHP model recapitulating disease progression to guide future translation of preclinical data to clinical study design.

Infectious disease modelling for SARS-CoV-2 in Africa to guide policy: A systematic review

Applied epidemiological models have played a critical role in understanding the transmission and control of disease outbreaks. Their utility and accuracy in decision-making on appropriate responses during public health emergencies is however a factor of their calibration to local data, evidence informing model assumptions, speed of obtaining and communicating their results, ease of understanding and willingness by policymakers to use their insights. We conducted a systematic review of infectious disease models focused on SARS-CoV-2 in Africa to determine: a) spatial and temporal patterns of SARS-CoV-2 modelling in Africa, b) use of local data to calibrate the models and local expertise in modelling activities, and c) key modelling questions and policy insights. We searched PubMed, Embase, Web of Science and MedRxiv databases following the PRISMA guidelines to obtain all SARS-CoV-2 dynamic modelling papers for one or multiple African countries. We extracted data on countries studied, authors and their affiliations, modelling questions addressed, type of models used, use of local data to calibrate the models, and model insights for guiding policy decisions. A total of 74 papers met the inclusion criteria, with nearly two-thirds of these coming from 6% (3) of the African countries. Initial papers were published 2 months after the first cases were reported in Africa, with most papers published after the first wave. More than half of all papers (53, 78%) and (48, 65%) had a first and last author affiliated to an African institution respectively, and only 12% (9) used local data for model calibration. A total of 60% (46) of the papers modelled assessment of control interventions. The transmission rate parameter was found to drive the most uncertainty in the sensitivity analysis for majority of the models. The use of dynamic models to draw policy insights was crucial and therefore there is need to increase modelling capacity in the continent.

Predicting the Effectiveness of Endemic Infectious Disease Control Interventions: The Impact of Mass Action versus Network Model Structure

BACKGROUND

Analyses of the effectiveness of infectious disease control interventions often rely on dynamic transmission models to simulate intervention effects. We aim to understand how the choice of network or compartmental model can influence estimates of intervention effectiveness in the short and long term for an endemic disease with susceptible and infected states in which infection, once contracted, is lifelong.

METHODS

We consider 4 disease models with different permutations of socially connected network versus unstructured contact (mass-action mixing) model and heterogeneous versus homogeneous disease risk. The models have susceptible and infected populations calibrated to the same long-term equilibrium disease prevalence. We consider a simple intervention with varying levels of coverage and efficacy that reduces transmission probabilities. We measure the rate of prevalence decline over the first 365 d after the intervention, long-term equilibrium prevalence, and long-term effective reproduction ratio at equilibrium.

RESULTS

Prevalence declined up to 10% faster in homogeneous risk models than heterogeneous risk models. When the disease was not eradicated, the long-term equilibrium disease prevalence was higher in mass-action mixing models than in network models by 40% or more. This difference in long-term equilibrium prevalence between network versus mass-action mixing models was greater than that of heterogeneous versus homogeneous risk models (less than 30%); network models tended to have higher effective reproduction ratios than mass-action mixing models for given combinations of intervention coverage and efficacy.

CONCLUSIONS

For interventions with high efficacy and coverage, mass-action mixing models could provide a sufficient estimate of effectiveness, whereas for interventions with low efficacy and coverage, or interventions in which outcomes are measured over short time horizons, predictions from network and mass-action models diverge, highlighting the importance of sensitivity analyses on model structure.

HIGHLIGHTS

• We calibrate 4 models-socially connected network versus unstructured contact (mass-action mixing) model and heterogeneous versus homogeneous disease risk-to 10% preintervention disease prevalence.• We measure the short- and long-term intervention effectiveness of all models using the rate of prevalence decline, long-term equilibrium disease prevalence, and effective reproduction ratio.• Generally, in the short term, prevalence declined faster in the homogeneous risk models than in the heterogeneous risk models.• Generally, in the long term, equilibrium disease prevalence was higher in the mass-action mixing models than in the network models, and the effective reproduction ratio was higher in network models than in the mass-action mixing models.

The Basic Reproduction Number as a Loop Gain Matrix

The COVID-19 pandemic and the disordered reactions of most governments made the importance of mathematical modelling and model-based predictions evident, even outside the scientific community. The basic reproduction number [Formula: see text] quickly entered the common jargon, as a concise but effective tool to communicate the spreading power of a disease and estimate, at least roughly, the possible outcomes of the epidemic. However, while [Formula: see text] is easily defined for simple models, its proper definition is more subtle for larger, state-of-the-art models. Here we show that it is nothing else than the spectral radius of the gain matrix of a linear system, and that this matrix generalizes [Formula: see text] in the computation of the vector-valued final epidemic size and epidemic threshold, in a large class of finite-dimensional SIR-like models.

Automated monitoring of tweets for early detection of the 2014 Ebola epidemic

First reported in March 2014, an Ebola epidemic impacted West Africa, most notably Liberia, Guinea and Sierra Leone. We demonstrate the value of social media for automated surveillance of infectious diseases such as the West Africa Ebola epidemic. We experiment with two variations of an existing surveillance architecture: the first aggregates tweets related to different symptoms together, while the second considers tweets about each symptom separately and then aggregates the set of alerts generated by the architecture. Using a dataset of tweets posted from the affected region from 2011 to 2014, we obtain alerts in December 2013, which is three months prior to the official announcement of the epidemic. Among the two variations, the second, which produces a restricted but useful set of alerts, can potentially be applied to other infectious disease surveillance and alert systems.

Estimating the impact of violent events on transmission in Ebola virus disease outbreak, Democratic Republic of the Congo, 2018-2019

INTRODUCTION

As of April 2019, the current Ebola virus disease (EVD) outbreak in the Democratic Republic of the Congo (DRC) is occurring in a longstanding conflict zone and has become the second largest EVD outbreak in history. It is suspected that after violent events occur, EVD transmission will increase; however, empirical studies to understand the impact of violence on transmission are lacking. Here, we use spatial and temporal trends of EVD case counts to compare transmission rates between health zones that have versus have not experienced recent violent events during the outbreak.

METHODS

We collected daily EVD case counts from DRC Ministry of Health. A time-varying indicator of recent violence in each health zone was derived from events documented in the WHO situation reports. We used the Wallinga-Teunis technique to estimate the reproduction number R for each case by day per zone in the 2018-2019 outbreak. We fit an exponentially decaying curve to estimates of R overall and by health zone, for comparison to past outbreaks.

RESULTS

As of 16 April 2019, the mean overall R for the entire outbreak was 1.11. We found evidence of an increase in the estimated transmission rates in health zones with recently reported violent events versus those without (p = 0.008). The average R was estimated as between 0.61 and 0.86 in regions not affected by recent violent events, and between 1.01 and 1.07 in zones affected by violent events within the last 21 days, leading to an increase in R between 0.17 and 0.53. Within zones with recent violent events, the mean estimated quenching rate was lower than for all past outbreaks except the 2013-2016 West African outbreak.

CONCLUSION

The difference in the estimated transmission rates between zones affected by recent violent events suggests that violent events are contributing to increased transmission and the ongoing nature of this outbreak.

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.

Precision Global Health - The case of Ebola: a scoping review

BACKGROUND

The 2014-2016 Ebola outbreak across West Africa was devastating, acting not only as a wake-up call for the global health community, but also as a catalyst for innovative change and global action. Improved infectious disease monitoring is the stepping-stone toward better disease prevention and control efforts, and recent research has revealed the potential of digital technologies to transform the field of global health. This scoping review aimed to identify which digital technologies may improve disease prevention and control, with regard to the 2014-2016 Ebola outbreak in West Africa.

METHODS

A search was conducted on PubMed, EBSCOhost and Web of Science, with search dates ranging from 2013 (01/01/2013) - 2017 (13/06/2017). Data was extracted into a summative table and data synthesized through grouping digital technology domains, using narrative and graphical methods.

FINDINGS

The scoping review identified 82 full-text articles, and revealed big data (48%, n = 39) and modeling (26%, n = 21) technologies to be the most utilized within the Ebola outbreak. Digital technologies were mainly used for surveillance purposes (90%, n = 74), and key challenges were related to scalability and misinformation from social media platforms.

INTERPRETATION

Digital technologies demonstrated their potential during the Ebola outbreak through: more rapid diagnostics, more precise predictions and estimations, increased knowledge transfer, and raising situational awareness through mHealth and social media platforms such as Twitter and Weibo. However, better integration into both citizen and health professionals' communities is necessary to maximise the potential of digital technologies.

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.

Cooperative system analysis of the Ebola virus epidemic model

This paper aims to study the global stability of an Ebola virus epidemic model. Although this epidemic ended in September 2015, it devastated several West African countries and mobilized the international community. With the recent cases of Ebola in the Democratic Republic of the Congo (DRC), the threat of the reappearance of this fatal disease remains. Therefore, we are obligated to be prepared for a possible re-emerging of the disease. In this work, we investigate the global stability analysis via the theory of cooperative systems, and we determine the conditions that lead to global stability diseases free and endemic equilibrium.

Best practice assessment of disease modelling for infectious disease outbreaks

During emerging disease outbreaks, public health, emergency management officials and decision-makers increasingly rely on epidemiological models to forecast outbreak progression and determine the best response to health crisis needs. Outbreak response strategies derived from such modelling may include pharmaceutical distribution, immunisation campaigns, social distancing, prophylactic pharmaceuticals, medical care, bed surge, security and other requirements. Infectious disease modelling estimates are unavoidably subject to multiple interpretations, and full understanding of a model's limitations may be lost when provided from the disease modeller to public health practitioner to government policymaker. We review epidemiological models created for diseases which are of greatest concern for public health protection. Such diseases, whether transmitted from person-to-person (Ebola, influenza, smallpox), via direct exposure (anthrax), or food and waterborne exposure (cholera, typhoid) may cause severe illness and death in a large population. We examine disease-specific models to determine best practices characterising infectious disease outbreaks and facilitating emergency response and implementation of public health policy and disease control measures.