The 2014-2015 Ebola Virus Disease (EVD) epidemic in West Africa was the largest ever recorded, representing a fundamental shift in Ebola epidemiology with unprecedented spatiotemporal complexity. We developed spatial transmission models using a gravity-model framework to explain spatiotemporal dynamics of EVD in West Africa at both the national and district-level scales, and to compare effectiveness of local interventions (e.g. local quarantine) and long-range interventions (e.g. border-closures). Incorporating spatial interactions, the gravity model successfully captures the multiple waves of epidemic growth observed in Guinea. Model simulations indicate that local-transmission reductions were most effective in Liberia, while long-range transmission was dominant in Sierra Leone. The model indicates the presence of spatial herd protection, wherein intervention in one region has a protective effect on surrounding regions. The district-level intervention analysis indicates the presence of intervention-amplifying regions, which provide above-expected levels of reduction in cases and deaths beyond their borders. The gravity-modeling approach accurately captured the spatial spread patterns of EVD at both country and district levels, and helps to identify the most effective locales for intervention. This model structure and intervention analysis provides information that can be used by public health policymakers to assist planning and response efforts for future epidemics.
Based on the reported data until 18 March 2015 and numerical fitting via a simple formula of cumulative case number, we provide real-time estimation on basic reproduction number, inflection point, peak time and final outbreak size of ongoing Ebola outbreak in West Africa. From our simulation, we conclude that the first wave has passed its inflection point and predict that a second epidemic wave may appear in the near future.
The Ebola virus in West Africa has infected almost 30,000 and killed over 11,000 people. Recent models of Ebola Virus Disease (EVD) have often made assumptions about how the disease spreads, such as uniform transmissibility and homogeneous mixing within a population. In this paper, we test whether these assumptions are necessarily correct, and offer simple solutions that may improve disease model accuracy. First, we use data and models of West African migration to show that EVD does not homogeneously mix, but spreads in a predictable manner. Next, we estimate the initial growth rate of EVD wit…
This paper investigates the dynamics of Ebola virus transmission in West Africa during 2014. The reproduction numbers for the total period of epidemic and for different consequent time intervals are estimated based on a newly suggested linear model. It contains one major variable - the average time of infectiousness (time from onset to hospitalization) that is considered as a parameter for controlling the future dynamics of epidemics. Numerical implementations are carried out on data collected from three countries Guinea, Sierra Leone and Liberia as well as the total data collected worldwide. …
A differential equations model is developed for the 2014 Ebola epidemics in Sierra Leone, Liberia, and Guinea. The model describes the dynamic interactions of the susceptible and infected populations of these countries. The model incorporates the principle features of contact tracing, namely, the number of contacts per identified infectious case, the likelihood that a traced contact is either incubating or infectious, and the efficiency of the contact tracing process.The model is first fitted to current cumulative reported case data in each country. The data fitted simulations are then project…
We use a multivariate formulation of sequential Monte Carlo filter that utilizes mechanistic models for Ebola virus propagation and available incidence data to simultaneously estimate the disease progression states and the model parameters. This method has the advantage of performing the inference online as the new data becomes available and estimates the evolution of basic reproductive ratio $R_0(t)$ of the Ebola outbreak through time. Our analysis identifies a peak in the basic reproductive ratio close to the time when Ebola cases were reported in Europe and the USA.
The 2014 Ebola virus (EBOV) outbreak in West Africa is the largest outbreak of the genus Ebolavirus to date. To better understand the spread of infection in the affected countries, it is crucial to know the number of secondary cases generated by an infected index case in the absence and presence of control measures, i.e., the basic and effective reproduction number. In this study, I describe the EBOV epidemic using an SEIR (susceptible-exposed-infectious-recovered) model and fit the model to the most recent reported data of infected cases and deaths in Guinea, Sierra Leone and Liberia. The max…
A model of an Ebola epidemic is developed with infected individuals structured according to disease age. The transmission of the infection is tracked by disease age through an initial incubation (exposed) phase, followed by an infectious phase with variable transmission infectiousness. The removal of infected individuals is dependent on disease age, with three types of removal rates: (1) removal due to hospitalization (isolation), (2) removal due to mortality separate from hospitalization, and (3) removal due to recovery separate from hospitalization. The model is applied to the Ebola epidemic…
West Africa is currently experiencing a severe outbreak of Ebola virus disease (EVD). As part of the international effort to address this outbreak, the United States has committed to building specialized Ebola treatment facilities with 1700 beds. However, the effectiveness of this increase in the available healthcare facilities to treat Ebola is unclear, especially in light of the rapidly increasing number of cases. Adapting a previously validated mathematical model of Ebola in West Africa, we examine the potential impact of an increase in hospital capacity to mitigate the impact of Ebola unde…
Background: While many infectious disease epidemics are initially characterized by an exponential growth in time, we show that district-level Ebola virus disease (EVD) outbreaks in West Africa follow slower polynomial-based growth kinetics over several generations of the disease. Methods: We analyzed epidemic growth patterns at three different spatial scales (regional, national, and subnational) of the Ebola virus disease epidemic in Guinea, Sierra Leone and Liberia by compiling publicly available weekly time series of reported EVD case numbers from the patient database available from the Worl…
The Ebola epidemic in West Africa is the largest ever recorded, with over 27,000 cases and 11,000 deaths as of June 2015. The public health response was challenged by difficulties with disease surveillance, which impacted subsequent analysis and decision-making regarding optimal interventions. We developed a stage-structured model of Ebola virus disease (EVD). A key feature of the model is that it includes a generalized correction term accounting for factors such as the fraction of cases reported and fraction of the population at risk (e.g. due to contact patterns, interventions, spatiotempora…
The spread of Ebola virus in 2014 is unprecedented. The epidemic is still affecting West Africa, exacerbated by extraordinary socioeconomic disadvantages and health system inadequacies. With the aim of understanding, predicting, and control the propagation of the virus in the populations of affected countries, it is crucial to model the dynamics of the virus and study several strategies to control it. In this paper, we present a very simple mathematical model that describes quite well the spread of Ebola. Then, we discuss several strategies for the control of the propagation of this lethal vir…
The Ebola virus is currently one of the most virulent pathogens for humans. The latest major outbreak occurred in Guinea, Sierra Leonne and Liberia in 2014. With the aim of understanding the spread of infection in the affected countries, it is crucial to modelize the virus and simulate it. In this paper, we begin by studying a simple mathematical model that describes the 2014 Ebola outbreak in Liberia. Then, we use numerical simulations and available data provided by the World Health Organization to validate the obtained mathematical model. Moreover, we develop a new mathematical model includi…
The most recent Ebola outbreak in West Africa highlighted critical weaknesses in the medical infrastructure of the affected countries, including effective diagnostics tools, sufficient isolation wards, and enough medical personnel. Here, we develop and analyze a mathematical model to assess the impact of early diagnosis of pre-symptomatic individuals on the transmission dynamics of Ebola virus disease in West Africa in scenarios where Ebola may remain at low levels in the population. Our findings highlight the importance of implementing integrated control measures of early diagnosis and isolat…
${\bf Background:}$ The early growth dynamics of the West African Ebola virus epidemic has been qualitatively different for Guinea, Sierra Leone and Liberia. However, it is important to understand these disparate dynamics as trends of a single epidemic spread over regions with similar geographic and cultural aspects, with likely common parameters for transmission rates and the reproduction number $R_0$. ${\bf Methods:}$ We combine a discrete, stochastic SEIR model with a two-scale community network model to demonstrate that the different regional trends may be explained by different community …
The data for the Ebola outbreak that occurred in 2014-2016 in three countries of West Africa are analysed within a common framework. The analysis is made using the results of an agent based Susceptible-Infected-Removed (SIR) model on a Euclidean network, where nodes at a distance $l$ are connected with probability $P(l) \propto l^{-δ}$, $δ$ determining the range of the interaction, in addition to nearest neighbors. The cumulative (total) density of infected population here has the form $R(t) = \frac{a\exp(t/T)}{1+c\exp(t/T)}$, where the parameters depend on $δ$ and the infection probability $q…
Multiple epidemiological models have been proposed to predict the spread of Ebola in West Africa. These models include consideration of counter-measures meant to slow and, eventually, stop the spread of the disease. Here, we examine one component of Ebola dynamics that is of growing concern -- the transmission of Ebola from the dead to the living. We do so by applying the toolkit of mathematical epidemiology to analyze the consequences of post-death transmission. We show that underlying disease parameters cannot be inferred with confidence from early-stage incidence data (that is, they are not…
An Ebola outbreak of unparalleled size is currently affecting several countries in West Africa, and international efforts to control the outbreak are underway. However, the efficacy of these interventions, and their likely impact on an Ebola epidemic of this size, is unknown. Forecasting and simulation of these interventions may inform public health efforts. We use existing data from Liberia and Sierra Leone to parameterize a mathematical model of Ebola and use this model to forecast the progression of the epidemic, as well as the efficacy of several interventions, including increased contact …
Containing the recent West African outbreak of Ebola virus (EBOV) required the deployment of substantial global resources. Operationally, health workers and surveillance teams treated cases, collected genetic samples, and tracked case contacts. Despite the substantial progress in analyzing and modeling EBOV epidemiological data, a complete characterization of the spatiotemporal spread of Ebola cases remains a challenge. In this work, we offer a novel perspective on the EBOV epidemic that utilizes virus genome sequences to inform population-level, spatial models. Calibrated to phylogenetic link…
Background: The 2014 Ebola outbreak in West Africa was the largest on record, resulting in over 25,000 total infections and 15,000 total deaths. Mathematical modeling can be used to investigate the mechanisms driving transmission during this outbreak -- in particular, burial practices appear to have been major source of infections. Methodology/Principal Findings: We developed a multi-stage model of Ebola virus transmission linked to a game-theoretic model of population burial practice selection. We fit our model to cumulative incidence and mortality data from Guinea, Liberia, and Sierra Leone …
A major Ebola outbreak occurs in West Africa since March 2014, being the deadliest epidemic in history. As an infectious disease epidemiology, Ebola is the most lethal and is moving faster than in previous outbreaks. On 8 August 2014, the World Health Organization (WHO) declared the outbreak a public health emergency of international concern. Last update on 7 July 2015 by WHO reports 27 609 cases of Ebola with a total of 11 261 deaths. In this work, we present a mathematical description of the spread of Ebola virus based on the SEIR (Susceptible-Exposed-Infective-Recovered) model and optimal s…
Dynamic models - often deterministic in nature - were used to estimate the basic reproductive number, R_0, of the 2014-5 Ebola virus disease (EVD) epidemic outbreak in West Africa. Estimates of R_0 were then used to project the likelihood for large outbreak sizes, e.g., exceeding hundreds of thousands of cases. Yet fitting deterministic models can lead to over-confidence in the confidence intervals of the fitted R_0, and, in turn, the type and scope of necessary interventions. In this manuscript we propose a hybrid stochastic-deterministic method to estimate R_0 and associated confidence inter…
In 2014, a major epidemic of human Ebola virus disease emerged in West Africa, where human-to-human transmission has now been been sustained for greater than 10 months. In the summer of 2014, there was great uncertainty about the answers to several key policy questions concerning the path to containment. In recent years, epidemic models have been used to guide public health interventions. But, model-based policy relies on high quality causal understanding of transmission, including the availability of appropriate dynamic transmission models and reliable reporting about the sequence of case inc…
Contact tracing is an important control strategy for containing Ebola epidemics. From a theoretical perspective, explicitly incorporating contact tracing with disease dynamics presents challenges, and population level effects of contact tracing are difficult to determine. In this work, we formulate and analyze a mechanistic SEIR type outbreak model which considers the key features of contact tracing, and we characterize the impact of contact tracing on the effective reproduction number, $\mathcal R_e$, of Ebola. In particular, we determine how relevant epidemiological properties such as incuba…
As an emergent infectious disease outbreak unfolds, public health response is reliant on information on key epidemiological quantities, such as transmission potential and serial interval. Increasingly, transmission models fit to incidence data are used to estimate these parameters and guide policy. Some widely-used modeling practices lead to potentially large errors in parameter estimates and, consequently, errors in model-based forecasts. Even more worryingly, in such situations, confidence in parameter estimates and forecasts can itself be far over-estimated, leading to the potential for lar…
The 2014 Ebola outbreak in west Africa raised many questions about the control of infectious disease in an increasingly connected global society. Limited availability of contact information made contact tracing difficult or impractical in combating the outbreak. We consider the development of multi-scale public health strategies and simulate policies for community-level response aimed at early screening of communities rather than individuals, as well as travel restrictions to prevent community cross-contamination. Our analysis shows the policies to be effective even at a relatively low level o…
Ebola virus disease is a lethal human and primate disease that currently requires a particular attention from the international health authorities due to important outbreaks in some Western African countries and isolated cases in the United Kingdom, the USA and Spain. Regarding the emergency of this situation, there is a need of development of decision tools, such as mathematical models, to assist the authorities to focus their efforts in important factors to eradicate Ebola. In this work, we propose a novel deterministic spatial-temporal model, called Be-CoDiS (Between-Countries Disease Sprea…
A better characterization of the early growth dynamics of an epidemic is needed to dissect the important drivers of disease transmission. We introduce a 2-parameter generalized-growth model to characterize the ascending phase of an outbreak and capture epidemic profiles ranging from sub-exponential to exponential growth. We test the model against empirical outbreak data representing a variety of viral pathogens and provide simulations highlighting the importance of sub-exponential growth for forecasting purposes. We applied the generalized-growth model to 20 infectious disease outbreaks repres…
