Modeling the impact of interventions on an epidemic of ebola in sierra leone and liberia

Sequence optimized diagnostic assay for Ebola virus detection

Rapid pathogen identification is a critical first step in patient isolation, treatment, and controlling an outbreak. Real-time PCR is a highly sensitive and specific approach commonly used for infectious disease diagnostics. However, mismatches in the primer or probe sequence and the target organism can cause decreased sensitivity, assay failure, and false negative results. Limited genomic sequences for rare pathogens such as Ebola virus (EBOV) can negatively impact assay performance due to undiscovered genetic diversity. We previously developed and validated several EBOV assays prior to the 2013-2016 EBOV outbreak in West Africa, and sequencing EBOV Makona identified sequence variants that could impact assay performance. Here, we assessed the impact sequence mismatches have on EBOV assay performance, finding one or two primer or probe mismatches resulted in a range of impact from minimal to almost two log sensitivity reduction. Redesigning this assay improved detection of all EBOV variants tested. Comparing the performance of the new assay with the previous assays across a panel of human EBOV samples confirmed increased assay sensitivity as reflected in decreased Cq values with detection of three positive that tested negative with the original assay.

Modelling the Role of Human Behaviour in Ebola Virus Disease (EVD) Transmission Dynamics

The role of human behaviour in the dynamics of infectious diseases cannot be underestimated. A clear understanding of how human behaviour influences the spread of infectious diseases is critical in establishing and designing control measures. To study the role that human behaviour plays in Ebola disease dynamics, in this paper, we design an Ebola virus disease model with disease transmission dynamics based on a new exponential nonlinear incidence function. This new incidence function that captures the reduction in disease transmission due to human behaviour innovatively considers the efficacy and the speed of behaviour change. The model's steady states are determined and suitable Lyapunov functions are built. The proofs of the global stability of equilibrium points are presented. To demonstrate the utility of the model, we fit the model to Ebola virus disease data from Liberia and Sierra Leone. The results which are comparable to existing findings from the outbreak of 2014 − 2016 show a better fit when the efficacy and the speed of behaviour change are higher. A rapid and efficacious behaviour change as a control measure to rapidly control an Ebola virus disease epidemic is advocated. Consequently, this model has implications for the management and control of future Ebola virus disease outbreaks.

Epidemiological and economic impact of COVID-19 in the US

This research measures the epidemiological and economic impact of COVID-19 spread in the US under different mitigation scenarios, comprising of non-pharmaceutical interventions. A detailed disease model of COVID-19 is combined with a model of the US economy to estimate the direct impact of labor supply shock to each sector arising from morbidity, mortality, and lockdown, as well as the indirect impact caused by the interdependencies between sectors. During a lockdown, estimates of jobs that are workable from home in each sector are used to modify the shock to labor supply. Results show trade-offs between economic losses, and lives saved and infections averted are non-linear in compliance to social distancing and the duration of the lockdown. Sectors that are worst hit are not the labor-intensive sectors such as the Agriculture sector and the Construction sector, but the ones with high valued jobs such as the Professional Services, even after the teleworkability of jobs is accounted for. Additionally, the findings show that a low compliance to interventions can be overcome by a longer shutdown period and vice versa to arrive at similar epidemiological impact but their net effect on economic loss depends on the interplay between the marginal gains from averting infections and deaths, versus the marginal loss from having healthy workers stay at home during the shutdown.

Agent-Based Computational Epidemiological Modeling

The study of epidemics is useful for not only understanding outbreaks and trying to limit their adverse effects, but also because epidemics are related to social phenomena such as government instability, crime, poverty, and inequality. One approach for studying epidemics is to simulate their spread through populations. In this work, we describe an integrated multi-dimensional approach to epidemic simulation, which encompasses: (1) a theoretical framework for simulation and analysis; (2) synthetic population (digital twin) generation; (3) (social contact) network construction methods from synthetic populations, (4) stylized network construction methods; and (5) simulation of the evolution of a virus or disease through a social network. We describe these aspects and end with a short discussion on simulation results that inform public policy.

Mesoscopic Modeling and Rapid Simulation of Incremental Changes in Epidemic Scenarios on GPUs: Fast What-If Analyses of Localized and Dynamic Effects

In simulation-based studies and analyses of epidemics, a major challenge lies in resolving the conflict between fidelity of models and the speed of their simulation. Another related challenge arises in dealing with the large number of what–if scenarios that need to be explored. Here, we describe new computational methods that together provide an approach to dealing with both challenges. A mesoscopic modeling approach is described that strikes a middle ground between macroscopic models based on coupled differential equations and microscopic models built on fine-grained behaviors at the individual entity level. The mesoscopic approach offers the ability to incorporate complex compositions of multiple layers of dynamics even while retaining the potential for aggregate behaviors at varying levels. It also is an excellent match to the accelerator-based architectures of modern computing platforms in which graphical processing units (GPUs) can be exploited for fast simulation via the parallel execution mode of single instruction multiple thread (SIMT). The challenge of simulating a large number of scenarios is addressed via a method of sharing model state and computation across a tree of what–if scenarios that are localized, incremental changes to a large base simulation. A combination of the mesoscopic modeling approach and the incremental what–if scenario tree evaluation has been implemented in the software on modern GPUs. Synthetic simulation scenarios are presented to demonstrate the computational characteristics of our approach. Results from the experiments with large population data, including USA, UK, and India, illustrate the modeling methodology and computational performance on thousands of synthetically generated what–if scenarios. Execution of our implementation scaled to 8192 GPUs of supercomputing platforms demonstrates the ability to rapidly evaluate what–if scenarios several orders of magnitude faster than the conventional methods.

A Mathematical Model of Contact Tracing during the 2014–2016 West African Ebola Outbreak

The 2014–2016 West African outbreak of Ebola Virus Disease (EVD) was the largest and most deadly to date. Contact tracing, following up those who may have been infected through contact with an infected individual to prevent secondary spread, plays a vital role in controlling such outbreaks. Our aim in this work was to mechanistically represent the contact tracing process to illustrate potential areas of improvement in managing contact tracing efforts. We also explored the role contact tracing played in eventually ending the outbreak. We present a system of ordinary differential equations to model contact tracing in Sierra Leonne during the outbreak. Using data on cumulative cases and deaths, we estimate most of the parameters in our model. We include the novel features of counting the total number of people being traced and tying this directly to the number of tracers doing this work. Our work highlights the importance of incorporating changing behavior into one’s model as needed when indicated by the data and reported trends. Our results show that a larger contact tracing program would have reduced the death toll of the outbreak. Counting the total number of people being traced and including changes in behavior in our model led to better understanding of disease management.

Stochastic Modeling of Plant Virus Propagation with Biological Control

Plants are vital for man and many species. They are sources of food, medicine, fiber for clothes and materials for shelter. They are a fundamental part of a healthy environment. However, plants are subject to virus diseases. In plants most of the virus propagation is done by a vector. The traditional way of controlling the insects is to use insecticides that have a negative effect on the environment. A more environmentally friendly way to control the insects is to use predators that will prey on the vector, such as birds or bats. In this paper we modify a plant-virus propagation model with delays. The model is written using delay differential equations. However, it can also be expressed in terms of biochemical reactions, which is more realistic for small populations. Since there are always variations in the populations, errors in the measured values and uncertainties, we use two methods to introduce randomness: stochastic differential equations and the Gillespie algorithm. We present numerical simulations. The Gillespie method produces good results for plant-virus population models.

Modeling and tracking Covid-19 cases using Big Data analytics on HPCC system platformm

This project is funded by the US National Science Foundation (NSF) through their NSF RAPID program under the title "Modeling Corona Spread Using Big Data Analytics." The project is a joint effort between the Department of Computer & Electrical Engineering and Computer Science at FAU and a research group from LexisNexis Risk Solutions. The novel coronavirus Covid-19 originated in China in early December 2019 and has rapidly spread to many countries around the globe, with the number of confirmed cases increasing every day. Covid-19 is officially a pandemic. It is a novel infection with serious clinical manifestations, including death, and it has reached at least 124 countries and territories. Although the ultimate course and impact of Covid-19 are uncertain, it is not merely possible but likely that the disease will produce enough severe illness to overwhelm the worldwide health care infrastructure. Emerging viral pandemics can place extraordinary and sustained demands on public health and health systems and on providers of essential community services. Modeling the Covid-19 pandemic spread is challenging. But there are data that can be used to project resource demands. Estimates of the reproductive number (R) of SARS-CoV-2 show that at the beginning of the epidemic, each infected person spreads the virus to at least two others, on average (Emanuel et al. in N Engl J Med. 2020, Livingston and Bucher in JAMA 323(14):1335, 2020). A conservatively low estimate is that 5 % of the population could become infected within 3 months. Preliminary data from China and Italy regarding the distribution of case severity and fatality vary widely (Wu and McGoogan in JAMA 323(13):1239-42, 2020). A recent large-scale analysis from China suggests that 80 % of those infected either are asymptomatic or have mild symptoms; a finding that implies that demand for advanced medical services might apply to only 20 % of the total infected. Of patients infected with Covid-19, about 15 % have severe illness and 5 % have critical illness (Emanuel et al. in N Engl J Med. 2020). Overall, mortality ranges from 0.25 % to as high as 3.0 % (Emanuel et al. in N Engl J Med. 2020, Wilson et al. in Emerg Infect Dis 26(6):1339, 2020). Case fatality rates are much higher for vulnerable populations, such as persons over the age of 80 years (> 14 %) and those with coexisting conditions (10 % for those with cardiovascular disease and 7 % for those with diabetes) (Emanuel et al. in N Engl J Med. 2020). Overall, Covid-19 is substantially deadlier than seasonal influenza, which has a mortality of roughly 0.1 %. Public health efforts depend heavily on predicting how diseases such as those caused by Covid-19 spread across the globe. During the early days of a new outbreak, when reliable data are still scarce, researchers turn to mathematical models that can predict where people who could be infected are going and how likely they are to bring the disease with them. These computational methods use known statistical equations that calculate the probability of individuals transmitting the illness. Modern computational power allows these models to quickly incorporate multiple inputs, such as a given disease's ability to pass from person to person and the movement patterns of potentially infected people traveling by air and land. This process sometimes involves making assumptions about unknown factors, such as an individual's exact travel pattern. By plugging in different possible versions of each input, however, researchers can update the models as new information becomes available and compare their results to observed patterns for the illness. In this paper we describe the development a model of Corona spread by using innovative big data analytics techniques and tools. We leveraged our experience from research in modeling Ebola spread (Shaw et al. Modeling Ebola Spread and Using HPCC/KEL System. In: Big Data Technologies and Applications 2016 (pp. 347-385). Springer, Cham) to successfully model Corona spread, we will obtain new results, and help in reducing the number of Corona patients. We closely collaborated with LexisNexis, which is a leading US data analytics company and a member of our NSF I/UCRC for Advanced Knowledge Enablement. The lack of a comprehensive view and informative analysis of the status of the pandemic can also cause panic and instability within society. Our work proposes the HPCC Systems Covid-19 tracker, which provides a multi-level view of the pandemic with the informative virus spreading indicators in a timely manner. The system embeds a classical epidemiological model known as SIR and spreading indicators based on causal model. The data solution of the tracker is built on top of the Big Data processing platform HPCC Systems, from ingesting and tracking of various data sources to fast delivery of the data to the public. The HPCC Systems Covid-19 tracker presents the Covid-19 data on a daily, weekly, and cumulative basis up to global-level and down to the county-level. It also provides statistical analysis for each level such as new cases per 100,000 population. The primary analysis such as Contagion Risk and Infection State is based on causal model with a seven-day sliding window. Our work has been released as a publicly available website to the world and attracted a great volume of traffic. The project is open-sourced and available on GitHub. The system was developed on the LexisNexis HPCC Systems, which is briefly described in the paper.

Analysing how changes in the health status of healthcare workers affects epidemic outcomes

During a disease outbreak, healthcare workers (HCWs) are essential to treat infected individuals. However, these HCWs are themselves susceptible to contracting the disease. As more HCWs get infected, fewer are available to provide care for others, and the overall quality of care available to infected individuals declines. This depletion of HCWs may contribute to the epidemic's severity. To examine this issue, we explicitly model declining quality of care in four differential equation-based susceptible, infected and recovered-type models with vaccination. We assume that vaccination, recovery and survival rates are affected by quality of care delivered. We show that explicitly modelling HCWs and accounting for declining quality of care significantly alters model-predicted disease outcomes, specifically case counts and mortality. Models neglecting the decline of quality of care resulting from infection of HCWs may significantly under-estimate cases and mortality. These models may be useful to inform health policy that may differ for HCWs and the general population. Models accounting for declining quality of care may therefore improve the management interventions considered to mitigate the effects of a future outbreak.

Epidemiological and Economic Impact of COVID-19 in the US

This research measures the epidemiological and economic impact of COVID-19 spread in the US under different mitigation scenarios, comprising of non-pharmaceutical interventions. A detailed disease model of COVID-19 is combined with a model of the US economy to estimate the direct impact of labor supply shock to each sector arising from morbidity, mortality, and lock down, as well as the indirect impact caused by the interdependencies between sectors. During a lockdown, estimates of jobs that are workable from home in each sector are used to modify the shock to labor supply. Results show trade-offs between economic losses, and lives saved and infections averted are non-linear in compliance to social distancing and the duration of lockdown. Sectors that are worst hit are not the labor-intensive sectors such as Agriculture and Construction, but the ones with high valued jobs such as Professional Services, even after the teleworkability of jobs is accounted for. Additionally, the findings show that a low compliance to interventions can be overcome by a longer shutdown period and vice versa to arrive at similar epidemiological impact but their net effect on economic loss depends on the interplay between the marginal gains from averting infections and deaths, versus the marginal loss from having healthy workers stay at home during the shutdown.

Methods for Rapid Mobility Estimation to Support Outbreak Response

When pressed for time, outbreak investigators often use homogeneous mixing models to model infectious diseases in data-poor regions. But recent outbreaks such as the 2014 Ebola outbreak in West Africa have shown the limitations of this approach in an era of increasing urbanization and connectivity. Both outbreak detection and predictive modeling depend on realistic estimates of human and disease mobility, but these data are difficult to acquire in a timely manner. This is especially true when dealing with an emerging outbreak in an under-resourced nation. Weighted travel networks with realistic estimates for population flows are often proprietary, expensive, or nonexistent. Here we propose a method for rapidly generating a mobility model from open-source data. As an example, we use road and river network data, along with population estimates, to construct a realistic model of human movement between health zones in the Democratic Republic of the Congo (DRC). Using these mobility data, we then fit an epidemic model to real-world surveillance data from the recent Ebola outbreak in the Nord Kivu region of the DRC to illustrate a potential use of the generated mobility estimation. In addition to providing a way for rapid risk estimation, this approach brings together novel techniques to merge diverse GIS datasets that can then be used to address issues that pertain to public health and global health security.

Medical costs of keeping the US economy open during COVID-19

We use an individual based model and national level epidemic simulations to estimate the medical costs of keeping the US economy open during COVID-19 pandemic under different counterfactual scenarios. We model an unmitigated scenario and 12 mitigation scenarios which differ in compliance behavior to social distancing strategies and in the duration of the stay-home order. Under each scenario we estimate the number of people who are likely to get infected and require medical attention, hospitalization, and ventilators. Given the per capita medical cost for each of these health states, we compute the total medical costs for each scenario and show the tradeoffs between deaths, costs, infections, compliance and the duration of stay-home order. We also consider the hospital bed capacity of each Hospital Referral Region (HRR) in the US to estimate the deficit in beds each HRR will likely encounter given the demand for hospital beds. We consider a case where HRRs share hospital beds among the neighboring HRRs during a surge in demand beyond the available beds and the impact it has in controlling additional deaths.

Modelling the daily risk of Ebola in the presence and absence of a potential vaccine

Ebola virus — one of the deadliest viral diseases, with a mortality rate around 90% — damages the immune system and organs, with symptoms including episodic fever, chills, malaise and myalgia. The Recombinant Vesicular Stomatitis Virus-based candidate vaccine (rVSV-ZEBOV) has demonstrated clinical efficacy against Ebola in ring-vaccination clinical trials. In order to evaluate the potential effect of this candidate vaccine, we developed risk equations for the daily risk of Ebola infection both currently and after vaccination. The risk equations account for the basic transmission probability of Ebola and the lowered risk due to various protection protocols: vaccination, hazmat suits, reduced contact with the infected living and dead bodies. Parameter space was sampled using Latin Hypercube Sampling, a statistical method for generating a near-random sample of parameter values. We found that at a high transmission rate of Ebola (i.e., if the transmission rate is greater than 90%), a large fraction of the population must be vaccinated (>80%) to achieve a 50% decrease in the daily risk of infection. If a vaccine is introduced, it must have at least 50% efficacy, and almost everyone in the affected areas must receive it to effectively control outbreaks of Ebola. These results indicate that a low-efficacy Ebola vaccine runs the risk of having vaccinated people be overconfident in a weak vaccine and hence the possibility that the vaccine could make the situation worse, unless the population can be sufficiently educated about the necessity for high vaccine uptake.

Controlling emerging zoonoses at the animal-human interface

BACKGROUND

For many emerging or re-emerging pathogens, cases in humans arise from a mixture of introductions (via zoonotic spillover from animal reservoirs or geographic spillover from endemic regions) and secondary human-to-human transmission. Interventions aiming to reduce incidence of these infections can be focused on preventing spillover or reducing human-to-human transmission, or sometimes both at once, and typically are governed by resource constraints that require policymakers to make choices. Despite increasing emphasis on using mathematical models to inform disease control policies, little attention has been paid to guiding rational disease control at the animal-human interface.

METHODS

We introduce a modeling framework to analyze the impacts of different disease control policies, focusing on pathogens exhibiting subcritical transmission among humans (i.e. pathogens that cannot establish sustained human-to-human transmission). We quantify the relative effectiveness of measures to reduce spillover (e.g. reducing contact with animal hosts), human-to-human transmission (e.g. case isolation), or both at once (e.g. vaccination), across a range of epidemiological contexts.

RESULTS

We provide guidelines for choosing which mode of control to prioritize in different epidemiological scenarios and considering different levels of resource and relative costs. We contextualize our analysis with current zoonotic pathogens and other subcritical pathogens, such as post-elimination measles, and control policies that have been applied.

CONCLUSIONS

Our work provides a model-based, theoretical foundation to understand and guide policy for subcritical zoonoses, integrating across disciplinary and species boundaries in a manner consistent with One Health principles.

Estimating the protective effect of case isolation with transmission tree reconstruction during the Ebola outbreak in Nigeria, 2014

The mainstream interventions used during the 2014-2016 Ebola epidemic were contact tracing and case isolation. The Ebola outbreak in Nigeria that formed part of the 2014-2016 epidemic demonstrated the effectiveness of control interventions with a 100% hospitalization rate. Here, we aim to explicitly estimate the protective effect of case isolation, reconstructing the time events of onset of illness and hospitalization as well as the transmission network. We show that case isolation reduced the reproduction number and shortened the serial interval. Employing Bayesian inference with the Markov chain Monte Carlo method for parameter estimation and assuming that the reproduction number exponentially declines over time, the protective effect of case isolation was estimated to be 39.7% (95% credible interval: 2.4%-82.1%). The individual protective effect of case isolation was also estimated, showing that the effectiveness was dependent on the speed, i.e. the time from onset of illness to hospitalization.

Medical Costs of Keeping the US Economy Open During COVID-19

We use an individual based model and national level epidemic simulations to estimate the medical costs of keeping the US economy open during COVID-19 pandemic under different counterfactual scenarios. We model an unmitigated scenario and 12 mitigation scenarios which differ in compliance behavior to social distancing strategies and to the duration of the stay-home order. Under each scenario we estimate the number of people who are likely to get infected and require medical attention, hospitalization, and ventilators. Given the per capita medical cost for each of these health states, we compute the total medical costs for each scenario and show the tradeoffs between deaths, costs, infections, compliance and the duration of stay-home order. We also consider the hospital bed capacity of each Hospital Referral Region (HRR) in the US to estimate the deficit in beds each HRR will likely encounter given the demand for hospital beds. We consider a case where HRRs share hospital beds among the neighboring HRRs during a surge in demand beyond the available beds and the impact it has in controlling additional deaths.

Multiscale model for the optimal design of pedestrian queues to mitigate infectious disease spread

There is direct evidence for the spread of infectious diseases such as influenza, SARS, measles, and norovirus in locations where large groups of people gather at high densities e.g. theme parks, airports, etc. The mixing of susceptible and infectious individuals in these high people density man-made environments involves pedestrian movement which is generally not taken into account in modeling studies of disease dynamics. We address this problem through a multiscale model that combines pedestrian dynamics with stochastic infection spread models. The pedestrian dynamics model is utilized to generate the trajectories of motion and contacts between infected and susceptible individuals. We incorporate this information into a stochastic infection dynamics model with infection probability and contact radius as primary inputs. This generic model is applicable for several directly transmitted diseases by varying the input parameters related to infectivity and transmission mechanisms. Through this multiscale framework, we estimate the aggregate numbers and probabilities of newly infected people for different winding queue configurations. We find that the queue configuration has a significant impact on disease spread for a range of infection radii and transmission probabilities. We quantify the effectiveness of wall separators in suppressing the disease spread compared to rope separators. Further, we find that configurations with short aisles lower the infection spread when rope separators are used.

Hybrid Modeling of Ebola Propagation

The Ebola virus disease (EVD) epidemic that occurred in West Africa between 2014-16 resulted in over 28,000 cases and 11,000 deaths - one of the deadliest to date. A generalized model of the spatiotemporal progression of EVD for Liberia, Guinea, and Sierra Leone in 2014-16 remains elusive. There is also a disconnect in the literature on which interventions are most effective in curbing disease progression. To solve these two key issues, we designed a hybrid agent-based and compartmental model that switches from one paradigm to the other on a stochastic threshold. We modeled disease progression with promising accuracy using WHO datasets.

Modelling the pandemic: attuning models to their contexts

The evidence produced in mathematical models plays a key role in shaping policy decisions in pandemics. A key question is therefore how well pandemic models relate to their implementation contexts. Drawing on the cases of Ebola and influenza, we map how sociological and anthropological research contributes in the modelling of pandemics to consider lessons for COVID-19. We show how models detach from their implementation contexts through their connections with global narratives of pandemic response, and how sociological and anthropological research can help to locate models differently. This potentiates multiple models of pandemic response attuned to their emerging situations in an iterative and adaptive science. We propose a more open approach to the modelling of pandemics which envisages the model as an intervention of deliberation in situations of evolving uncertainty. This challenges the 'business-as-usual' of evidence-based approaches in global health by accentuating all science, within and beyond pandemics, as 'emergent' and 'adaptive'.

Perfect counterfactuals for epidemic simulations

Simulation studies are often used to predict the expected impact of control measures in infectious disease outbreaks. Typically, two independent sets of simulations are conducted, one with the intervention, and one without, and epidemic sizes (or some related metric) are compared to estimate the effect of the intervention. Since it is possible that controlled epidemics are larger than uncontrolled ones if there is substantial stochastic variation between epidemics, uncertainty intervals from this approach can include a negative effect even for an effective intervention. To more precisely estimate the number of cases an intervention will prevent within a single epidemic, here we develop a 'single-world' approach to matching simulations of controlled epidemics to their exact uncontrolled counterfactual. Our method borrows concepts from percolation approaches, prunes out possible epidemic histories and creates potential epidemic graphs (i.e. a mathematical representation of all consistent epidemics) that can be 'realized' to create perfectly matched controlled and uncontrolled epidemics. We present an implementation of this method for a common class of compartmental models (e.g. SIR models), and its application in a simple SIR model. Results illustrate how, at the cost of some computation time, this method substantially narrows confidence intervals and avoids nonsensical inferences. 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'.

Adequacy of SEIR models when epidemics have spatial structure: Ebola in Sierra Leone

Dynamic SEIR (Susceptible, Exposed, Infectious, Removed) compartmental models provide a tool for predicting the size and duration of both unfettered and managed outbreaks-the latter in the context of interventions such as case detection, patient isolation, vaccination and treatment. The reliability of this tool depends on the validity of key assumptions that include homogeneity of individuals and spatio-temporal homogeneity. Although the SEIR compartmental framework can easily be extended to include demographic (e.g. age) and additional disease (e.g. healthcare workers) classes, dependence of transmission rates on time, and metapopulation structure, fitting such extended models is hampered by both a proliferation of free parameters and insufficient or inappropriate data. This raises the question of how effective a tool the basic SEIR framework may actually be. We go some way here to answering this question in the context of the 2014-2015 outbreak of Ebola in West Africa by comparing fits of an SEIR time-dependent transmission model to both country- and district-level weekly incidence data. Our novel approach in estimating the effective-size-of-the-populations-at-risk ( N_eff) and initial number of exposed individuals ( E₀) at both district and country levels, as well as the transmission function parameters, including a time-to-halving-the-force-of-infection ( t_f/2) parameter, provides new insights into this Ebola outbreak. It reveals that the estimate R₀ ≈ 1.7 from country-level data appears to seriously underestimate R₀ ≈ 3.3 - 4.3 obtained from more spatially homogeneous district-level data. Country-level data also overestimate t_f/2 ≈ 22 weeks, compared with 8-10 weeks from district-level data. Additionally, estimates for the duration of individual infectiousness is around two weeks from spatially inhomogeneous country-level data compared with 2.4-4.5 weeks from spatially more homogeneous district-level data, which estimates are rather high compared with most values reported in the literature. 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'.

Costs and benefits of early response in the Ebola virus disease outbreak in Sierra Leone

Background

The 2014–2016 Ebola virus disease (EVD) outbreak in West Africa was the largest EVD outbreak recorded, which has triggered calls for investments that would facilitate an even earlier response. This study aims to estimate the costs and health effects of earlier interventions in Sierra Leone.

Methods

A deterministic and a stochastic compartment model describing the EVD outbreak was estimated using a variety of data sources. Costs and Disability-Adjusted Life Years were used to estimate and compare scenarios of earlier interventions.

Results

Four weeks earlier interventions would have averted 10,257 (IQR 4353–18,813) cases and 8835 (IQR 3766–16,316) deaths. This implies 456 (IQR 194–841) thousand DALYs and 203 (IQR 87–374) million $US saved. The greatest losses occurred outside the healthcare sector.

Conclusions

Earlier response in an Ebola outbreak saves lives and costs. Investments in healthcare system facilitating such responses are needed and can offer good value for money.

Risk assessment of Ebola virus disease spreading in Uganda using a two-layer temporal network

Network-based modelling of infectious diseases apply compartmental models on a contact network, which makes the epidemic process crucially dependent on the network structure. For highly contagious diseases such as Ebola virus disease (EVD), interpersonal contact plays the most vital role in human-to-human transmission. Therefore, for accurate representation of EVD spreading, the contact network needs to resemble the reality. Prior research has mainly focused on static networks (only permanent contacts) or activity-driven networks (only temporal contacts) for Ebola spreading. A comprehensive network for EVD spreading should include both these network structures, as there are always some permanent contacts together with temporal contacts. Therefore, we propose a two-layer temporal network for Uganda, which is at risk of an Ebola outbreak from the neighboring Democratic Republic of Congo (DRC) epidemic. The network has a permanent layer representing permanent contacts among individuals within the family level, and a data-driven temporal network for human movements motivated by cattle trade, fish trade, or general communications. We propose a Gillespie algorithm with the susceptible-infected-recovered (SIR) compartmental model to simulate the evolution of EVD spreading as well as to evaluate the risk throughout our network. As an example, we applied our method to a network consisting of 23 districts along different movement routes in Uganda starting from bordering districts of the DRC to Kampala. Simulation results show that some regions are at higher risk of infection, suggesting some focal points for Ebola preparedness and providing direction to inform interventions in the field. Simulation results also show that decreasing physical contact as well as increasing preventive measures result in a reduction of chances to develop an outbreak. Overall, the main contribution of this paper lies in the novel method for risk assessment, which can be more precise with an increasing volume of accurate data for creating the network model.

Modeling outbreak data: Analysis of a 2012 Ebola virus disease epidemic in DRC

We describe two approaches to modeling data from a small to moderate-sized epidemic outbreak. The first approach is based on a branching process approximation and direct analysis of the transmission network, whereas the second one is based on a survival model derived from the classical SIR equations with no explicit transmission information. We compare these approaches using data from a 2012 outbreak of Ebola virus disease caused by Bundibugyo ebolavirus in city of Isiro, Democratic Republic of the Congo. The branching process model allows for a direct comparison of disease transmission across different environments, such as the general community or the Ebola treatment unit. However, the survival model appears to yield parameter estimates with more accuracy and better precision in some circumstances.

Impacts of environmental and socio-economic factors on emergence and epidemic potential of Ebola in Africa

Recent outbreaks of animal-borne emerging infectious diseases have likely been precipitated by a complex interplay of changing ecological, epidemiological and socio-economic factors. Here, we develop modelling methods that capture elements of each of these factors, to predict the risk of Ebola virus disease (EVD) across time and space. Our modelling results match previously-observed outbreak patterns with high accuracy, and suggest further outbreaks could occur across most of West and Central Africa. Trends in the underlying drivers of EVD risk suggest a 1.75 to 3.2-fold increase in the endemic rate of animal-human viral spill-overs in Africa by 2070, given current modes of healthcare intervention. Future global change scenarios with higher human population growth and lower rates of socio-economic development yield a fourfold higher likelihood of epidemics occurring as a result of spill-over events. Our modelling framework can be used to target interventions designed to reduce epidemic risk for many zoonotic diseases.

Assessing the value of PCR assays in oral fluid samples for detecting African swine fever, classical swine fever, and foot-and-mouth disease in U.S. swine

Introduction

Oral fluid sampling and testing offers a convenient, unobtrusive mechanism for evaluating the health status of swine, especially grower and finisher swine. This assessment evaluates the potential testing of oral fluid samples with real-time reverse-transcriptase polymerase chain reaction (rRT-PCR) to detect African swine fever, classical swine fever, or foot-and-mouth disease for surveillance during a disease outbreak and early detection in a disease-free setting.

Methods

We used a series of logical arguments, informed assumptions, and a range of parameter values from literature and industry practices to examine the cost and value of information provided by oral fluid sampling and rRT-PCR testing for the swine foreign animal disease surveillance objectives outlined above.

Results

Based on the evaluation, oral fluid testing demonstrated value for both settings evaluated. The greatest value was in an outbreak scenario, where using oral fluids would minimize disruption of animal and farm activities, reduce sample sizes by 23%-40%, and decrease resource requirements relative to current individual animal sampling plans. For an early detection system, sampling every 3 days met the designed prevalence detection threshold with 0.95 probability, but was quite costly.

Limitations

Implementation of oral fluid testing for African swine fever, classical swine fever, or foot-and-mouth disease surveillance is not yet possible due to several limitations and information gaps. The gaps include validation of PCR diagnostic protocols and kits for African swine fever, classical swine fever, or foot-and-mouth disease on swine oral fluid samples; minimal information on test performance in a field setting; detection windows with low virulence strains of some foreign animal disease viruses; and the need for confirmatory testing protocol development.

Parameter identification for a stochastic SEIRS epidemic model: case study influenza

A recent parameter identification technique, the local lagged adapted generalized method of moments, is used to identify the time-dependent disease transmission rate and time-dependent noise for the stochastic susceptible, exposed, infectious, temporarily immune, susceptible disease model (SEIRS) with vital rates. The stochasticity appears in the model due to fluctuations in the time-dependent transmission rate of the disease. All other parameter values are assumed to be fixed, known constants. The method is demonstrated with US influenza data from the 2004-2005 through 2016-2017 influenza seasons. The transmission rate and noise intensity stochastically work together to generate the yearly peaks in infections. The local lagged adapted generalized method of moments is tested for forecasting ability. Forecasts are made for the 2016-2017 influenza season and for infection data in year 2017. The forecast method qualitatively matches a single influenza season. Confidence intervals are given for possible future infectious levels.

Data Fitting and Scenario Analysis of Vaccination in the 2014 Ebola Outbreak in Liberia

Objectives

This study aimed to extend an epidemiological model (SEIHFR) to analyze epidemic trends, and evaluate intervention efficacy.

Methods

SEIHFR was modified to examine disease transmission dynamics after vaccination for the Ebola outbreak. Using existing data from Liberia, sensitivity analysis of various epidemic scenarios was used to inform the model structure, estimate the basic reproduction number ℜ₀ and investigate how the vaccination could effectively change the course of the epidemic.

Results

If a randomized mass vaccination strategy was adopted, vaccines would be administered prophylactically or as early as possible (depending on the availability of vaccines). An effective vaccination rate threshold for Liberia was estimated as 48.74% among susceptible individuals. If a ring vaccination strategy was adopted to control the spread of the Ebola virus, vaccines would be given to reduce the transmission rate improving the tracing rate of the contact persons of an infected individual.

Conclusion

The extended SEIHFR model predicted the total number of infected cases, number of deaths, number of recoveries, and duration of outbreaks among others with different levels of interventions such as vaccination rate. This model may be used to better understand the spread of Ebola and develop strategies that may achieve a disease-free state.

Concurrent assessment of epidemiological and operational uncertainties for optimal outbreak control: Ebola as a case study

Determining how best to manage an infectious disease outbreak may be hindered by both epidemiological uncertainty (i.e. about epidemiological processes) and operational uncertainty (i.e. about the effectiveness of candidate interventions). However, these two uncertainties are rarely addressed concurrently in epidemic studies. We present an approach to simultaneously address both sources of uncertainty, to elucidate which source most impedes decision-making. In the case of the 2014 West African Ebola outbreak, epidemiological uncertainty is represented by a large ensemble of published models. Operational uncertainty about three classes of interventions is assessed for a wide range of potential intervention effectiveness. We ranked each intervention by caseload reduction in each model, initially assuming an unlimited budget as a counterfactual. We then assessed the influence of three candidate cost functions relating intervention effectiveness and cost for different budget levels. The improvement in management outcomes to be gained by resolving uncertainty is generally high in this study; appropriate information gain could reduce expected caseload by more than 50%. The ranking of interventions is jointly determined by the underlying epidemiological process, the effectiveness of the interventions and the size of the budget. An epidemiologically effective intervention might not be optimal if its costs outweigh its epidemiological benefit. Under higher-budget conditions, resolution of epidemiological uncertainty is most valuable. When budgets are tight, however, operational and epidemiological uncertainty are equally important. Overall, our study demonstrates that significant reductions in caseload could result from a careful examination of both epidemiological and operational uncertainties within the same modelling structure. This approach can be applied to decision-making for the management of other diseases for which multiple models and multiple interventions are available.

A Network-Based Compartmental Model For The Spread Of Whooping Cough In Nebraska

Outbreaks of pertussis have increased over the past few years, drawing the attention of health care providers. Un- derstanding the transmission mechanisms of contagious disease is critically important, but depends on many intricate factors including pathogen and host environment, exposed population, and their activities. In this work, we try to improve upon the prediction model for the exposed population. The number of whooping cough reported cases in Nebraska between 2000-2017 was gathered. The standard Susceptible-Exposed-Infected-Recovered (SEIR) model is used to predict the infected numbers. The results show that the SEIR model prediction for the number of infected indi- viduals is much higher than the actual number. To overcome this problem, the Network Based-SEIR model is proposed, and is able to estimate the number of infected more accurately than the classic SEIR model.

Modeling the impact of quarantine during an outbreak of Ebola virus disease

The quarantine of people suspected of being exposed to an infectious agent is one of the most basic public health measure that has historically been used to combat the spread of communicable diseases in human communities. This study presents a new deterministic model for assessing the population-level impact of the quarantine of individuals suspected of being exposed to disease on the spread of the 2014-2015 outbreaks of Ebola viral disease. It is assumed that quarantine is imperfect (i.e., individuals can acquire infection during quarantine). In the absence of quarantine, the model is shown to exhibit global dynamics with respect to the disease-free and its unique endemic equilibrium when a certain epidemiological threshold (denoted byR 0 ) is either less than or greater than unity. Thus, unlike the full model with imperfect quarantine (which is known to exhibit the phenomenon of backward bifurcation), the version of the model with no quarantine does not undergo a backward bifurcation. Using data relevant to the 2014-2015 Ebola transmission dynamics in the three West African countries (Guinea, Liberia and Sierra Leone), uncertainty analysis of the model show that, although the current level and effectiveness of quarantine can lead to significant reduction in disease burden, they fail to bring the associated quarantine reproduction number (R 0 Q ) to a value less than unity (which is needed to make effective disease control or elimination feasible). This reduction ofR 0 Q is, however, very possible with a modest increase in quarantine rate and effectiveness. It is further shown, via sensitivity analysis, that the parameters related to the effectiveness of quarantine (namely the parameter associated with the reduction in infectiousness of infected quarantined individuals and the contact rate during quarantine) are the main drivers of the disease transmission dynamics. Overall, this study shows that the singular implementation of a quarantine intervention strategy can lead to the effective control or elimination of Ebola viral disease in a community if its coverage and effectiveness levels are high enough.

Discovery of under immunized spatial clusters using network scan statistics

BACKGROUND

Clusters of under-vaccinated children are emerging in a number of states in the United States due to rising rates of vaccine hesitancy and refusal. As the measles outbreaks in California and other states in 2015 and in Minnesota in 2017 showed, such clusters can pose a significant public health risk. Prior methods have used publicly-available school immunization data for analysis (except for a few, which use private healthcare patient records). School immunization data has limited demographic information-as a result, such analyses are not able to provide demographic characteristics of significant clusters. Further, the resolution of the clusters identified by prior methods is limited since they are typically restricted to disks or well-rounded shapes.

METHODS

We use realistic population models for Minnesota (MN) and Washington (WA) state, which provide a model of activities for all individuals in the population. We combine this with school level immunization data for these two states, to estimate vaccine coverage at the level of census block groups. A scan statistic method defined on networks is used for finding significant clusters of under-immunized block groups, without any restrictions on shape. Further we provide the demographic characteristics of these clusters.

RESULTS

We find 2 significant under-vaccinated clusters in MN and 3 in WA. These are very irregular in shape, in contrast to the circular disks reported in prior work, which rely on the SatScan approach. Some of the clusters found by our method are not contained in those computed using SatScan, a state-of-the-art software tool used in similar studies in other states.

CONCLUSIONS

The emergence of under-immunized clusters is a growing concern for public health agencies because they can act as reservoirs of infection and increase the risk of infection into the wider population. Higher resolution clusters computed using our network based approach and population models provide new insights on the structure and characteristics of such clusters and enable targeted interventions.

Assessing the performance of real-time epidemic forecasts: A case study of Ebola in the Western Area region of Sierra Leone, 2014-15

Real-time forecasts based on mathematical models can inform critical decision-making during infectious disease outbreaks. Yet, epidemic forecasts are rarely evaluated during or after the event, and there is little guidance on the best metrics for assessment. Here, we propose an evaluation approach that disentangles different components of forecasting ability using metrics that separately assess the calibration, sharpness and bias of forecasts. This makes it possible to assess not just how close a forecast was to reality but also how well uncertainty has been quantified. We used this approach to analyse the performance of weekly forecasts we generated in real time for Western Area, Sierra Leone, during the 2013-16 Ebola epidemic in West Africa. We investigated a range of forecast model variants based on the model fits generated at the time with a semi-mechanistic model, and found that good probabilistic calibration was achievable at short time horizons of one or two weeks ahead but model predictions were increasingly unreliable at longer forecasting horizons. This suggests that forecasts may have been of good enough quality to inform decision making based on predictions a few weeks ahead of time but not longer, reflecting the high level of uncertainty in the processes driving the trajectory of the epidemic. Comparing forecasts based on the semi-mechanistic model to simpler null models showed that the best semi-mechanistic model variant performed better than the null models with respect to probabilistic calibration, and that this would have been identified from the earliest stages of the outbreak. As forecasts become a routine part of the toolkit in public health, standards for evaluation of performance will be important for assessing quality and improving credibility of mathematical models, and for elucidating difficulties and trade-offs when aiming to make the most useful and reliable forecasts.

Epidemic Models of Contact Tracing: Systematic Review of Transmission Studies of Severe Acute Respiratory Syndrome and Middle East Respiratory Syndrome

The emergence and reemergence of coronavirus epidemics sparked renewed concerns from global epidemiology researchers and public health administrators. Mathematical models that represented how contact tracing and follow-up may control Severe Acute Respiratory Syndrome (SARS) and Middle East Respiratory Syndrome (MERS) transmissions were developed for evaluating different infection control interventions, estimating likely number of infections as well as facilitating understanding of their likely epidemiology. We reviewed mathematical models for contact tracing and follow-up control measures of SARS and MERS transmission. Model characteristics, epidemiological parameters and intervention parameters used in the mathematical models from seven studies were summarized. A major concern identified in future epidemics is whether public health administrators can collect all the required data for building epidemiological models in a short period of time during the early phase of an outbreak. Also, currently available models do not explicitly model constrained resources. We urge for closed-loop communication between public health administrators and modelling researchers to come up with guidelines to delineate the collection of the required data in the midst of an outbreak and the inclusion of additional logistical details in future similar models.

Efficacy of control measures in the control of Ebola, Liberia 2014-2015

The largest outbreak of Ebola to date is the 2014 West Africa Ebola outbreak, with more than 10,000 cases and over 4000 deaths reported in Liberia alone. To control the spread of the outbreak, multiple interventions were implemented: identification and isolation of cases, contact tracing, quarantining of suspected contacts, proper personal protection, safely conducted burials, improved education, social awareness and individual protective measures. Devising rigorous methodologies for the evaluation of the effectiveness of the control measures implemented to stop an outbreak is of paramount importance. In this paper, we evaluate the effectiveness of the 2014 Ebola outbreak interventions. We rely on model selection to determine the best model that explains the 2014 Ebola outbreak data in Liberia which is the simplest model with a social distancing term. We couple structural and practical identifiability analysis with the computation of confidence intervals to pinpoint the uncertainty in the parameter estimations. Finally, we evaluate the efficacy of control measures using the Ebola model with social distancing. Among all the control measures, we find that social distancing had the most impact on the control of the 2014 Ebola epidemic in Libreria followed by isolation and quarantining.

The large graph limit of a stochastic epidemic model on a dynamic multilayer network

We consider a Markovian SIR-type (Susceptible → Infected → Recovered) stochastic epidemic process with multiple modes of transmission on a contact network. The network is given by a random graph following a multilayer configuration model where edges in different layers correspond to potentially infectious contacts of different types. We assume that the graph structure evolves in response to the epidemic via activation or deactivation of edges of infectious nodes. We derive a large graph limit theorem that gives a system of ordinary differential equations (ODEs) describing the evolution of quantities of interest, such as the proportions of infected and susceptible vertices, as the number of nodes tends to infinity. Analysis of the limiting system elucidates how the coupling of edge activation and deactivation to infection status affects disease dynamics, as illustrated by a two-layer network example with edge types corresponding to community and healthcare contacts. Our theorem extends some earlier results describing the deterministic limit of stochastic SIR processes on static, single-layer configuration model graphs. We also describe precisely the conditions for equivalence between our limiting ODEs and the systems obtained via pair approximation, which are widely used in the epidemiological and ecological literature to approximate disease dynamics on networks. The flexible modeling framework and asymptotic results have potential application to many disease settings including Ebola dynamics in West Africa, which was the original motivation for this study.

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.

The potential impact of a prophylactic vaccine for Ebola in Sierra Leone

The 2014 outbreak of Ebola virus disease (EVD) in West Africa was multinational and of an unprecedented scale primarily affecting the countries of Guinea, Liberia, and Sierra Leone. One of the qualities that makes EVD of high public concern is its potential for extremely high mortality rates (up to 90%). A prophylactic vaccine for ebolavirus (rVSV-ZEBOV) has been developed, and clinical trials show near-perfect efficacy. We have developed an ordinary differential equations model that simulates an EVD epidemic and takes into account (1) transmission through contact with infectious EVD individuals and deceased EVD bodies, (2) the heterogeneity of the risk of becoming infected with EVD, and (3) the increased survival rate of infected EVD patients due to greater access to trained healthcare providers. Using fitted parameter values that closely simulate the dynamics of the 2014 outbreak in Sierra Leone, we utilize our model to predict the potential impact of a prophylactic vaccine for the ebolavirus using various vaccination strategies including ring vaccination. Our results show that an rVSV-ZEBOV vaccination coverage as low as 40% in the general population and 95% in healthcare workers will prevent another catastrophic outbreak like the 2014 outbreak from occurring.

Opportunities and challenges for modelling epidemiological and evolutionary dynamics in a multihost, multiparasite system: Zoonotic hybrid schistosomiasis in West Africa

Multihost multiparasite systems are evolutionarily and ecologically dynamic, which presents substantial trans-disciplinary challenges for elucidating their epidemiology and designing appropriate control. Evidence for hybridizations and introgressions between parasite species is gathering, in part in line with improvements in molecular diagnostics and genome sequencing. One major system where this is becoming apparent is within the Genus Schistosoma, where schistosomiasis represents a disease of considerable medical and veterinary importance, the greatest burden of which occurs in sub-Saharan Africa. Interspecific hybridizations and introgressions bring an increased level of complexity over and above that already inherent within multihost, multiparasite systems, also representing an additional source of genetic variation that can drive evolution. This has the potential for profound implications for the control of parasitic diseases, including, but not exclusive to, widening host range, increased transmission potential and altered responses to drug therapy. Here, we present the challenging case example of haematobium group Schistosoma spp. hybrids in West Africa, a system involving multiple interacting parasites and multiple definitive hosts, in a region where zoonotic reservoirs of schistosomiasis were not previously considered to be of importance. We consider how existing mathematical model frameworks for schistosome transmission could be expanded and adapted to zoonotic hybrid systems, exploring how such model frameworks can utilize molecular and epidemiological data, as well as the complexities and challenges this presents. We also highlight the opportunities and value such mathematical models could bring to this and a range of similar multihost, multi and cross-hybridizing parasites systems in our changing world.

Resilience management during large-scale epidemic outbreaks

Assessing and managing the impact of large-scale epidemics considering only the individual risk and severity of the disease is exceedingly difficult and could be extremely expensive. Economic consequences, infrastructure and service disruption, as well as the recovery speed, are just a few of the many dimensions along which to quantify the effect of an epidemic on society's fabric. Here, we extend the concept of resilience to characterize epidemics in structured populations, by defining the system-wide critical functionality that combines an individual's risk of getting the disease (disease attack rate) and the disruption to the system's functionality (human mobility deterioration). By studying both conceptual and data-driven models, we show that the integrated consideration of individual risks and societal disruptions under resilience assessment framework provides an insightful picture of how an epidemic might impact society. In particular, containment interventions intended for a straightforward reduction of the risk may have net negative impact on the system by slowing down the recovery of basic societal functions. The presented study operationalizes the resilience framework, providing a more nuanced and comprehensive approach for optimizing containment schemes and mitigation policies in the case of epidemic outbreaks.

An Exploration of the Spatiotemporal and Demographic Patterns of Ebola Virus Disease Epidemic in West Africa Using Open Access Data Sources

The purpose of this study was to investigate the utility of exploratory analytical techniques using publically available data in informing interventions in case of infectious diseases outbreaks. More exactly spatiotemporal and multivariate methods were used to characterize the dynamics of the Ebola Virus Disease (EVD) epidemic in West Africa, and propose plausible relationships with demographic/social risk factors. The analysis showed that there was significant spatial, temporal, and spatiotemporal dependence in the evolution of the disease. For the first part of the epidemic, the cases were highly clustered in a few administrative units, in the proximity of the point of origin of the outbreak, possibly offering the opportunity to stop the spread of the disease. Later in the epidemic, high clusters were observed, but only in Liberia and Sierra Leone. Although not definitely factors of risk, in the setting in which the epidemic arose, our analysis suggests infrastructure, access to and use of health services, and connectivity possibly accelerated and magnified the spread of EVD. Also, the spatial, temporal, and spatiotemporal patterns of epidemic can be clearly shown - with evident application in the early stages of management of epidemics. In particular, we found that the spatial-temporal analytic tool SaTScan may be used effectively during the evolution of an epidemic to identify areas for targeted intervention. In the case of EVD epidemic in West Africa, better data and integration local knowledge and customs may have been more useful to recognize the proper response.

The Ebola outbreak, 2013-2016: old lessons for new epidemics

Ebola virus causes a severe haemorrhagic fever in humans with high case fatality and significant epidemic potential. The 2013-2016 outbreak in West Africa was unprecedented in scale, being larger than all previous outbreaks combined, with 28 646 reported cases and 11 323 reported deaths. It was also unique in its geographical distribution and multicountry spread. It is vital that the lessons learned from the world's largest Ebola outbreak are not lost. This article aims to provide a detailed description of the evolution of the outbreak. We contextualize this outbreak in relation to previous Ebola outbreaks and outline the theories regarding its origins and emergence. The outbreak is described by country, in chronological order, including epidemiological parameters and implementation of outbreak containment strategies. We then summarize the factors that led to rapid and extensive propagation, as well as highlight the key successes, failures and lessons learned from this outbreak and the response.This article is part of the themed issue 'The 2013-2016 West African Ebola epidemic: data, decision-making and disease control'.

Application of a quantitative entry assessment model to compare the relative risk of incursion of zoonotic bat-borne viruses into European Union Member States

This paper presents a quantitative assessment model for the risk of entry of zoonotic bat-borne viruses into the European Union (EU). The model considers four routes of introduction: human travel, legal trade of products, live animal imports and illegal import of bushmeat and was applied to five virus outbreak scenarios. Two scenarios were considered for Zaire ebolavirus (wEBOV, cEBOV) and other scenarios for Hendra virus, Marburg virus (MARV) and Middle East Respiratory Syndrome Coronavirus (MERS-CoV). The use of the same framework and generic data sources for all EU Member States (MS) allows for a relative comparison of the probability of virus introduction and of the importance of the routes of introduction among MSs. According to the model wEBOV posed the highest risk of an introduction event within the EU, followed by MARV and MERS-CoV. However, the main route of introduction differed, with wEBOV and MERS-CoV most likely through human travel and MARV through legal trade of foodstuffs. The relative risks to EU MSs as entry points also varied between outbreak scenarios, highlighting the heterogeneity in global trade and travel to the EU MSs. The model has the capability to allow for a continual updating of the risk estimate using new data as, and when, it becomes available. The model provides an horizon scanning tool for use when available data are limited and, therefore, the absolute risk estimates often have high uncertainty. Sensitivity analysis suggested virus prevalence in bats has a large influence on the results; a 90% reduction in prevalence reduced the risk of introduction considerably and resulted in the relative ranking of MARV falling below that for MERS-CoV, due to this parameter disproportionately affecting the risk of introduction from the trade route over human travel.

The RAPIDD Ebola forecasting challenge: Model description and synthetic data generation

The Ebola forecasting challenge organized by the Research and Policy for Infectious Disease Dynamics (RAPIDD) program of the Fogarty International Center relies on synthetic disease datasets generated by numerical simulations of a highly detailed spatially-structured agent-based model. We discuss here the architecture and technical steps of the challenge, leading to datasets that mimic as much as possible the data collection, reporting, and communication process experienced in the 2014-2015 West African Ebola outbreak. We provide a detailed discussion of the model's definition, the epidemiological scenarios' construction, synthetic patient database generation and the data communication platform used during the challenge. Finally we offer a number of considerations and takeaways concerning the extension and scalability of synthetic challenges to other infectious diseases.

Integrative modelling for One Health: pattern, process and participation

This paper argues for an integrative modelling approach for understanding zoonoses disease dynamics, combining process, pattern and participatory models. Each type of modelling provides important insights, but all are limited. Combining these in a '3P' approach offers the opportunity for a productive conversation between modelling efforts, contributing to a 'One Health' agenda. The aim is not to come up with a composite model, but seek synergies between perspectives, encouraging cross-disciplinary interactions. We illustrate our argument with cases from Africa, and in particular from our work on Ebola virus and Lassa fever virus. Combining process-based compartmental models with macroecological data offers a spatial perspective on potential disease impacts. However, without insights from the ground, the 'black box' of transmission dynamics, so crucial to model assumptions, may not be fully understood. We show how participatory modelling and ethnographic research of Ebola and Lassa fever can reveal social roles, unsafe practices, mobility and movement and temporal changes in livelihoods. Together with longer-term dynamics of change in societies and ecologies, all can be important in explaining disease transmission, and provide important complementary insights to other modelling efforts. An integrative modelling approach therefore can offer help to improve disease control efforts and public health responses.This article is part of the themed issue 'One Health for a changing world: zoonoses, ecosystems and human well-being'.

Estimating the number of secondary Ebola cases resulting from an unsafe burial and risk factors for transmission during the West Africa Ebola epidemic

Background

Safely burying Ebola infected individuals is acknowledged to be important for controlling Ebola epidemics and was a major component of the 2013–2016 West Africa Ebola response. Yet, in order to understand the impact of safe burial programs it is necessary to elucidate the role of unsafe burials in sustaining chains of Ebola transmission and how the risk posed by activities surrounding unsafe burials, including care provided at home prior to death, vary with human behavior and geography.

Methodology/Principal findings

Interviews with next of kin and community members were carried out for unsafe burials in Sierra Leone, Liberia and Guinea, in six districts where the Red Cross was responsible for safe and dignified burials (SDB). Districts were randomly selected from a district-specific sampling frame comprised of villages and neighborhoods that had experienced cases of Ebola. An average of 2.58 secondary cases were potentially generated per unsafe burial and varied by district (range: 0–20). Contact before and after death was reported for 142 (46%) contacts. Caregivers of a primary case were 2.63 to 5.92 times more likely to become EVD infected compared to those with post-mortem contact only. Using these estimates, the Red Cross SDB program potentially averted between 1,411 and 10,452 secondary EVD cases, reducing the epidemic by 4.9% to 36.5%.

Conclusions/Significance

SDB is a fundamental control measure that limits community transmission of Ebola; however, for those individuals having contact before and after death, it was impossible to ascertain the exposure that caused their infection. The number of infections prevented through SDB is significant, yet greater impact would be achieved by early hospitalization of the primary case during acute illness.

The care of an individual infected with Ebola virus disease (EVD), their death, funeral, and burial in the community rather than in an Ebola Treatment Center (ETC) poses a serious risk for continued disease transmission. Consequently, SDB is an essential component of EVD outbreak response; however, its impact on transmission is not well understood. During the 2013–2016 EVD epidemic the Red Cross carried out over 50% of the official burials in Guinea, Liberia and Sierra Leone. We performed epidemiological investigations in EVD affected communities to better understand disease transmission linked to unsafe burials of (suspect) EVD infected individuals, and risk factors for transmission linked to caring and burial practices. An average of 2.58 secondary cases were potentially generated per unsafe burial investigated and varied by district (range: 0–20). Additionally, the Red Cross SDB program potentially averted between 1,411 and 10,452 secondary EVD cases, reducing the epidemic by 4.9% to 36.5%. Our results quantify for the first time the potential impact this essential EVD response component had on the 2013–2016 epidemic and highlight the importance of SDB as a fundamental control measure, while also underlining the well-known importance of isolating EVD infected individuals as soon as they show symptoms in order to limit transmission.

Assessment of the severity of Ebola virus disease in Sierra Leone in 2014-2015

The current Ebola virus disease (EVD) epidemic in West Africa is unprecedented in scale, and Sierra Leone is the most severely affected country. The case fatality risk (CFR) and hospitalization fatality risk (HFR) were used to characterize the severity of infections in confirmed and probable EVD cases in Sierra Leone. Proportional hazards regression models were used to investigate factors associated with the risk of death in EVD cases. In total, there were 17 318 EVD cases reported in Sierra Leone from 23 May 2014 to 31 January 2015. Of the probable and confirmed EVD cases with a reported final outcome, a total of 2536 deaths and 886 recoveries were reported. CFR and HFR estimates were 74·2% [95% credibility interval (CrI) 72·6-75·5] and 68·9% (95% CrI 66·2-71·6), respectively. Risks of death were higher in the youngest (0-4 years) and oldest (⩾60 years) age groups, and in the calendar month of October 2014. Sex and occupational status did not significantly affect the mortality of EVD. The CFR and HFR estimates of EVD were very high in Sierra Leone.

Mathematical models for devising the optimal Ebola virus disease eradication

BACKGROUND

The 2014-2015 epidemic of Ebola virus disease (EVD) in West Africa defines an unprecedented health threat for human.

METHODS

We construct a mathematical model to devise the optimal Ebola virus disease eradication plan. We used mathematical model to investigate the numerical spread of Ebola and eradication pathways, further fit our model against the real total cases data and calculated infection rate as 1.754.

RESULTS

With incorporating hospital isolation and application of medication in our model and analyzing their effect on resisting the spread, we demonstrate the second peak of 10,029 total cases in 23 days, and expect to eradicate EVD in 285 days. Using the regional spread of EVD with our transmission model analysis, we analyzed the numbers of new infections through four important transmission paths including household, community, hospital and unsafe funeral.

CONCLUSIONS

Based on the result of the model, we find out the key paths in different situations and propose our suggestion to control regional transmission. We fully considers Ebola characteristics, economic and time optimization, dynamic factors and local condition constraints, and to make our plan realistic, sensible and feasible.