Spatiotemporal Evolution of Ebola Virus Disease at Sub-National Level during the 2014 West Africa Epidemic: Model Scrutiny and Data Meagreness

A model for social spreading of Covid-19: Cases of Mexico, Finland and Iceland

The shocking severity of the Covid-19 pandemic has woken up an unprecedented interest and accelerated effort of the scientific community to model and forecast epidemic spreading to find ways to control it regionally and between regions. Here we present a model that in addition to describing the dynamics of epidemic spreading with the traditional compartmental approach takes into account the social behaviour of the population distributed over a geographical region. The region to be modelled is defined as a two-dimensional grid of cells, in which each cell is weighted with the population density. In each cell a compartmental SEIRS system of delay difference equations is used to simulate the local dynamics of the disease. The infections between cells are modelled by a network of connections, which could be terrestrial, between neighbouring cells, or long range, between cities by air, road or train traffic. In addition, since people make trips without apparent reason, noise is considered to account for them to carry contagion between two randomly chosen distant cells. Hence, there is a clear separation of the parameters related to the biological characteristics of the disease from the ones that represent the spatial spread of infections due to social behaviour. We demonstrate that these parameters provide sufficient information to trace the evolution of the pandemic in different situations. In order to show the predictive power of this kind of approach we have chosen three, in a number of ways different countries, Mexico, Finland and Iceland, in which the pandemics have followed different dynamic paths. Furthermore we find that our model seems quite capable of reproducing the path of the pandemic for months with few initial data. Unlike similar models, our model shows the emergence of multiple waves in the case when the disease becomes endemic.

Data and Digital Solutions to Support Surveillance Strategies in the Context of the COVID-19 Pandemic

Background: In order to prevent spread and improve control of infectious diseases, public health experts need to closely monitor human and animal populations. Infectious disease surveillance is an established, routine data collection process essential for early warning, rapid response, and disease control. The quantity of data potentially useful for early warning and surveillance has increased exponentially due to social media and other big data streams. Digital epidemiology is a novel discipline that includes harvesting, analysing, and interpreting data that were not initially collected for healthcare needs to enhance traditional surveillance. During the current COVID-19 pandemic, the importance of digital epidemiology complementing traditional public health approaches has been highlighted. Objective: The aim of this paper is to provide a comprehensive overview for the application of data and digital solutions to support surveillance strategies and draw implications for surveillance in the context of the COVID-19 pandemic and beyond. Methods: A search was conducted in PubMed databases. Articles published between January 2005 and May 2020 on the use of digital solutions to support surveillance strategies in pandemic settings and health emergencies were evaluated. Results: In this paper, we provide a comprehensive overview of digital epidemiology, available data sources, and components of 21st-century digital surveillance, early warning and response, outbreak management and control, and digital interventions. Conclusions: Our main purpose was to highlight the plausible use of new surveillance strategies, with implications for the COVID-19 pandemic strategies and then to identify opportunities and challenges for the successful development and implementation of digital solutions during non-emergency times of routine surveillance, with readiness for early-warning and response for future pandemics. The enhancement of traditional surveillance systems with novel digital surveillance methods opens a direction for the most effective framework for preparedness and response to future pandemics.

Multi-population stochastic modeling of Ebola in Sierra Leone: Investigation of spatial heterogeneity

A major outbreak of the Ebola virus occurred in 2014 in Sierra Leone. We investigate the spatial heterogeneity of the outbreak among districts in Sierra Leone. The stochastic discrete-time susceptible-exposed-infectious-removed (SEIR) model is used, allowing for probabilistic movements from one compartment to another. Our model accounts for heterogeneity among districts by making use of a hierarchical approach. The transmission rates are considered time-varying. It is investigated whether or not incubation period, infectious period and transmission rates are different among districts. Estimation is done using the Bayesian formalism. The posterior estimates of the effective reproductive number were substantially different across the districts, with pronounced variability in districts with few cases of Ebola. The posterior estimates of the reproductive number at the district level varied between below 1.0 and 4.5, whereas at nationwide level it varied between below 1.0 and 2.5. The posterior estimate of the effective reproductive number reached a value below 1.0 around December. In some districts, the effective reproductive number pointed out for the persistence of the outbreak or for a likely resurgence of new cases of Ebola virus disease (EVD). The posterior estimates have shown to be highly sensitive to prior elicitation, mainly the incubation period and infectious period.

A simple model for the total number of SARS-CoV-2 infections on a national level

This study aimed to identify an appropriate simple mathematical model to fit the number of coronavirus disease 2019 (COVID-19) cases at the national level for the early portion of the pandemic, before significant public health interventions could be enacted. The total number of cases for the COVID-19 epidemic over time in 28 countries was analysed and fit to several simple rate models. The resulting model parameters were used to extrapolate projections for more recent data. While the Gompertz growth model (mean R2 = 0.998) best fit the current data, uncertainties in the eventual case limit introduced significant model errors. However, the quadratic rate model (mean R2 = 0.992) fit the current data best for 25 (89%) countries as determined by R2 values of the remaining models. Projection to the future using the simple quadratic model accurately forecast the number of future total number of cases 50% of the time up to 10 days in advance. Extrapolation to the future with the simple exponential model significantly overpredicted the total number of future cases. These results demonstrate that accurate future predictions of the case load in a given country can be made using this very simple model.

On an SE(Is)(Ih)AR epidemic model with combined vaccination and antiviral controls for COVID-19 pandemic

In this paper, we study the nonnegativity and stability properties of the solutions of a newly proposed extended SEIR epidemic model, the so-called SE(Is)(Ih)AR epidemic model which might be of potential interest in the characterization and control of the COVID-19 pandemic evolution. The proposed model incorporates both asymptomatic infectious and hospitalized infectious subpopulations to the standard infectious subpopulation of the classical SEIR model. In parallel, it also incorporates feedback vaccination and antiviral treatment controls. The exposed subpopulation has three different transitions to the three kinds of infectious subpopulations under eventually different proportionality parameters. The existence of a unique disease-free equilibrium point and a unique endemic one is proved together with the calculation of their explicit components. Their local asymptotic stability properties and the attainability of the endemic equilibrium point are investigated based on the next generation matrix properties, the value of the basic reproduction number, and nonnegativity properties of the solution and its equilibrium states. The reproduction numbers in the presence of one or both controls is linked to the control-free reproduction number to emphasize that such a number decreases with the control gains. We also prove that, depending on the value of the basic reproduction number, only one of them is a global asymptotic attractor and that the solution has no limit cycles.

On a Controlled Se(Is)(Ih)(Iicu)AR Epidemic Model with Output Controllability Issues to Satisfy Hospital Constraints on Hospitalized Patients

An epidemic model, the so-called SE(Is)(Ih)(Iicu)AR epidemic model, is proposed which splits the infectious subpopulation of the classical SEIR (Susceptible-Exposed-Infectious-Recovered) model into four subpopulations, namely asymptomatic infectious and three categories of symptomatic infectious, namely slight infectious, non-intensive care infectious, and intensive care hospitalized infectious. The exposed subpopulation has four different transitions to each one of the four kinds of infectious subpopulations governed under eventually different proportionality parameters. The performed research relies on the problem of satisfying prescribed hospitalization constraints related to the number of patients via control interventions. There are four potential available controls which can be manipulated, namely the vaccination of the susceptible individuals, the treatment of the non-intensive care unit hospitalized patients, the treatment of the hospitalized patients at the intensive care unit, and the transmission rate which can be eventually updated via public interventions such as isolation of the infectious, rules of groups meetings, use of face masks, decrees of partial or total quarantines, and others. The patients staying at the non-intensive care unit and those staying at the intensive care unit are eventually, but not necessarily, managed as two different hospitalized subpopulations. The controls are designed based on output controllability issues in the sense that the levels of hospital admissions are constrained via prescribed maximum levels and the measurable outputs are defined by the hospitalized patients either under a joint consideration of the sum of both subpopulations or separately. In this second case, it is possible to target any of the two hospitalized subpopulations only or both of them considered as two different components of the output. Different algorithms are given to design the controls which guarantee, if possible, that the prescribed hospitalization constraints hold. If this were not possible, because the levels of serious infection are too high according to the hospital availability means, then the constraints are revised and modified accordingly so that the amended ones could be satisfied by a set of controls. The algorithms are tested through numerically worked examples under disease parameterizations of COVID-19.

Infectious diseases epidemiology, quantitative methodology, and clinical research in the midst of the COVID-19 pandemic: Perspective from a European country

Starting from historic reflections, the current SARS-CoV-2 induced COVID-19 pandemic is examined from various perspectives, in terms of what it implies for the implementation of non-pharmaceutical interventions, the modeling and monitoring of the epidemic, the development of early-warning systems, the study of mortality, prevalence estimation, diagnostic and serological testing, vaccine development, and ultimately clinical trials. Emphasis is placed on how the pandemic had led to unprecedented speed in methodological and clinical development, the pitfalls thereof, but also the opportunities that it engenders for national and international collaboration, and how it has simplified and sped up procedures. We also study the impact of the pandemic on clinical trials in other indications. We note that it has placed biostatistics, epidemiology, virology, infectiology, and vaccinology, and related fields in the spotlight in an unprecedented way, implying great opportunities, but also the need to communicate effectively, often amidst controversy.

Game analysis on the evolution of COVID-19 epidemic under the prevention and control measures of the government

In this paper, the interaction strategies and the evolutionary game analysis of the actions taken by the government and the public in the early days of the epidemic are incorporated into the natural transmission mechanism model of the epidemic, and then the transmission frequency equations of COVID-19 epidemic is established. According to the cumulative confirmed cases of COVID-19 in the UK and China, the upper limit of the spread of COVID-19 in different evolutionary scenarios is set. Using SPSS to perform logistic curve fitting, the frequency fitting equations of cumulative confirmed cases under different evolution scenarios are obtained respectively. The analysis result shows that the emergency response strategy adopted by the government in the early days of the epidemic can effectively control the spread of the epidemic. Combined with the transmission frequency equation of COVID-19 epidemic, measures taken by the government are analyzed. The influence of each measure on the frequency variable is judged and then the influence on the spread of the epidemic is obtained. Finally, based on the above analysis, the government is advised to adhere to the principles of scientific, initiative and flexibility when facing major epidemics.

Piecewise quadratic growth during the 2019 novel coronavirus epidemic

The temporal growth in the number of deaths in the COVID-19 epidemic is subexponential. Here we show that a piecewise quadratic law provides an excellent fit during the thirty days after the first three fatalities on January 20 and later since the end of March 2020. There is also a brief intermediate period of exponential growth. During the second quadratic growth phase, the characteristic time of the growth is about eight times shorter than in the beginning, which can be understood as the occurrence of separate hotspots. Quadratic behavior can be motivated by peripheral growth when further spreading occurs only on the outskirts of an infected region. We also study numerical solutions of a simple epidemic model, where the spatial extend of the system is taken into account. To model the delayed onset outside China together with the early one in China within a single model with minimal assumptions, we adopt an initial condition of several hotspots, of which one reaches saturation much earlier than the others. At each site, quadratic growth commences when the local number of infections has reached a certain saturation level. The total number of deaths does then indeed follow a piecewise quadratic behavior.

Control of Ebola virus disease outbreaks: Comparison of health care worker-targeted and community vaccination strategies

BACKGROUND

Health care workers (HCW) are at risk of infection during Ebola virus disease outbreaks and therefore may be targeted for vaccination before or during outbreaks. The effect of these strategies depends on the role of HCW in transmission which is understudied.

METHODS

To evaluate the effect of HCW-targeted or community vaccination strategies, we used a transmission model to explore the relative contribution of HCW and the community to transmission. We calibrated the model to data from multiple Ebola outbreaks. We quantified the impact of ahead-of-time HCW-targeted strategies, and reactive HCW and community vaccination.

RESULTS

We found that for some outbreaks (we call "type 1″) HCW amplified transmission both to other HCW and the community, and in these outbreaks prophylactic vaccination of HCW decreased outbreak size. Reactive vaccination strategies had little effect because type 1 outbreaks ended quickly. However, in outbreaks with longer time courses ("type 2 outbreaks"), reactive community vaccination decreased the number of cases, with or without prophylactic HCW-targeted vaccination. For both outbreak types, we found that ahead-of-time HCW-targeted strategies had an impact at coverage of 30%.

CONCLUSIONS

The vaccine strategies tested had a different impact depending on the transmission dynamics and previous control measures. Although we will not know the characteristics of a new outbreak, ahead-of-time HCW-targeted vaccination can decrease the total outbreak size, even at low vaccine coverage.

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

BACKGROUND

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

METHODS

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

FINDINGS

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

INTERPRETATION

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

On a New Discrete SEIADR Model with Mixed Controls: Study of Its Properties

A new discrete SEIADR epidemic model is built based on previous continuous models. The model considers two extra subpopulation, namely, asymptomatic and lying corpses on the usual SEIR models. It can be of potential interest for diseases where infected corpses are infectious like, for instance, Ebola. The model includes two types of vaccinations, a constant one and another proportional to the susceptible subpopulation, as well as a treatment control applied to the infected subpopulation. We study the positivity of the controlled model and the stability of the equilibrium points. Simulations are made in order to provide allocation and examples to the different possible conditions. The equilibrium point with no infection and its stability is related, via the reproduction number values, to the reachability of the endemic equilibrium point.

Assessing the relationship between epidemic growth scaling and epidemic size: The 2014-16 Ebola epidemic in West Africa

We assess the relationship between epidemic size and the scaling of epidemic growth of Ebola epidemics at the level of administrative areas during the 2014-16 Ebola epidemic in West Africa. For this purpose, we quantify growth scaling parameters from the ascending phase of Ebola outbreaks comprising at least 7 weeks of epidemic growth. We then study how these parameters are associated with observed epidemic sizes. For validation purposes, we also analyse two historic Ebola outbreaks. We find a high monotonic association between the scaling of epidemic growth parameter and the observed epidemic size. For example, scaling of growth parameters around 0.3-0.4, 0.4-0.6 and 0.6 are associated with epidemic sizes on the order of 350-460, 460-840 and 840-2500 cases, respectively. These results are not explained by differences in epidemic onset across affected areas. We also find the relationship between the scaling of epidemic growth parameter and the observed epidemic size to be consistent for two past Ebola outbreaks in Congo (1976) and Uganda (2000). Signature features of epidemic growth could become useful to assess the risk of observing a major epidemic outbreak, generate improved diseases forecasts and enhance the predictive power of epidemic models. Our results indicate that the epidemic growth scaling parameter is a useful indicator of epidemic size, which may have significant implications to guide control of Ebola outbreaks and possibly other infectious diseases.

Dynamics of Zika virus outbreaks: an overview of mathematical modeling approaches

BACKGROUND

The Zika virus was first discovered in 1947. It was neglected until a major outbreak occurred on Yap Island, Micronesia, in 2007. Teratogenic effects resulting in microcephaly in newborn infants is the greatest public health threat. In 2016, the Zika virus epidemic was declared as a Public Health Emergency of International Concern (PHEIC). Consequently, mathematical models were constructed to explicitly elucidate related transmission dynamics.

SURVEY METHODOLOGY

In this review article, two steps of journal article searching were performed. First, we attempted to identify mathematical models previously applied to the study of vector-borne diseases using the search terms "dynamics," "mathematical model," "modeling," and "vector-borne" together with the names of vector-borne diseases including chikungunya, dengue, malaria, West Nile, and Zika. Then the identified types of model were further investigated. Second, we narrowed down our survey to focus on only Zika virus research. The terms we searched for were "compartmental," "spatial," "metapopulation," "network," "individual-based," "agent-based" AND "Zika." All relevant studies were included regardless of the year of publication. We have collected research articles that were published before August 2017 based on our search criteria. In this publication survey, we explored the Google Scholar and PubMed databases.

RESULTS

We found five basic model architectures previously applied to vector-borne virus studies, particularly in Zika virus simulations. These include compartmental, spatial, metapopulation, network, and individual-based models. We found that Zika models carried out for early epidemics were mostly fit into compartmental structures and were less complicated compared to the more recent ones. Simple models are still commonly used for the timely assessment of epidemics. Nevertheless, due to the availability of large-scale real-world data and computational power, recently there has been growing interest in more complex modeling frameworks.

DISCUSSION

Mathematical models are employed to explore and predict how an infectious disease spreads in the real world, evaluate the disease importation risk, and assess the effectiveness of intervention strategies. As the trends in modeling of infectious diseases have been shifting towards data-driven approaches, simple and complex models should be exploited differently. Simple models can be produced in a timely fashion to provide an estimation of the possible impacts. In contrast, complex models integrating real-world data require more time to develop but are far more realistic. The preparation of complicated modeling frameworks prior to the outbreaks is recommended, including the case of future Zika epidemic preparation.

Modeling spatial invasion of Ebola in West Africa

The 2014-2016 Ebola Virus Disease (EVD) epidemic in West Africa was the largest ever recorded, representing a fundamental shift in Ebola epidemiology with unprecedented spatiotemporal complexity. To understand the spatiotemporal dynamics of EVD in West Africa, we developed spatial transmission models using a gravity-model framework at both the national and district-level scales, which we used to compare effectiveness of local interventions (e.g. local quarantine) and long-range interventions (e.g. border-closures). The country-level gravity model captures the epidemic data, including multiple waves of initial epidemic growth observed in Guinea. We found that local-transmission reductions were most effective in Liberia, while long-range transmission was dominant in Sierra Leone. Both models illustrated that interventions in one region result in an amplified protective effect on other regions by preventing spatial transmission. In the district-level model, interventions in the strongest of these amplifying regions reduced total cases in all three countries by over 20%, in spite of the region itself generating only ∼0.1% of total cases. This model structure and associated intervention analysis provide information that can be used by public health policymakers to assist planning and response efforts for future epidemics.

Mathematical models to characterize early epidemic growth: A review

There is a long tradition of using mathematical models to generate insights into the transmission dynamics of infectious diseases and assess the potential impact of different intervention strategies. The increasing use of mathematical models for epidemic forecasting has highlighted the importance of designing reliable models that capture the baseline transmission characteristics of specific pathogens and social contexts. More refined models are needed however, in particular to account for variation in the early growth dynamics of real epidemics and to gain a better understanding of the mechanisms at play. Here, we review recent progress on modeling and characterizing early epidemic growth patterns from infectious disease outbreak data, and survey the types of mathematical formulations that are most useful for capturing a diversity of early epidemic growth profiles, ranging from sub-exponential to exponential growth dynamics. Specifically, we review mathematical models that incorporate spatial details or realistic population mixing structures, including meta-population models, individual-based network models, and simple SIR-type models that incorporate the effects of reactive behavior changes or inhomogeneous mixing. In this process, we also analyze simulation data stemming from detailed large-scale agent-based models previously designed and calibrated to study how realistic social networks and disease transmission characteristics shape early epidemic growth patterns, general transmission dynamics, and control of international disease emergencies such as the 2009 A/H1N1 influenza pandemic and the 2014-2015 Ebola epidemic in West Africa.

Heterogeneity in District-Level Transmission of Ebola Virus Disease during the 2013-2015 Epidemic in West Africa

The Ebola virus disease (EVD) epidemic in West Africa in 2013-2015 spread heterogeneously across the three hardest-hit countries Guinea, Liberia and Sierra Leone and the estimation of national transmission of EVD provides little information about local dynamics. To investigate district-level transmissibility of EVD, we applied a statistical modelling approach to estimate the basic reproduction number (R0) for each affected district and each country using weekly incident case numbers. We estimated growth rates during the early exponential phase of the outbreak using exponential regression of the case counts on the first eight weeks since onset. To take into account the heterogeneity between and within countries, we fitted a mixed effects model and calculated R0 based on the predicted individual growth rates and the reported serial interval distribution. At district level, R0 ranged from 0.36 (Dubréka) to 1.72 (Beyla) in Guinea, from 0.53 (Maryland) to 3.37 (Margibi) in Liberia and from 1.14 (Koinadugu) to 2.73 (Western Rural) in Sierra Leone. At national level, we estimated an R0 of 0.97 (95% CI 0.77-1.18) for Guinea, 1.26 (95% CI 0.98-1.55) for Liberia and 1.66 (95% CI 1.32-2.00) for Sierra Leone. Socio-demographic variables related to urbanisation such as high population density and high wealth index were found positively associated with R0 suggesting that the consequences of fast urban growth in West Africa may have contributed to the increased spread of EVD.