Evidence Synthesis for Stochastic Epidemic Models

Dynamic Hybrid Model to Forecast the Spread of COVID-19 Using LSTM and Behavioral Models Under Uncertainty

To accurately predict the regional spread of coronavirus disease 2019 (COVID-19) infection, this study proposes a novel hybrid model, which combines a long short-term memory (LSTM) artificial recurrent neural network with dynamic behavioral models. Several factors and control strategies affect the virus spread, and the uncertainty arising from confounding variables underlying the spread of the COVID-19 infection is substantial. The proposed model considers the effect of multiple factors to enhance the accuracy in predicting the number of cases and deaths across the top ten most-affected countries at the time of the study. The results show that the proposed model closely replicates the test data, such that not only it provides accurate predictions but it also replicates the daily behavior of the system under uncertainty. The hybrid model outperforms the LSTM model while accounting for data limitation. The parameters of the hybrid models are optimized using a genetic algorithm for each country to improve the prediction power while considering regional properties. Since the proposed model can accurately predict the short-term to medium-term daily spreading of the COVID-19 infection, it is capable of being used for policy assessment, planning, and decision making.

Inferring the spread of COVID-19: the role of time-varying reporting rate in epidemiological modelling

The role of epidemiological models is crucial for informing public health officials during a public health emergency, such as the COVID-19 pandemic. However, traditional epidemiological models fail to capture the time-varying effects of mitigation strategies and do not account for under-reporting of active cases, thus introducing bias in the estimation of model parameters. To infer more accurate parameter estimates and to reduce the uncertainty of these estimates, we extend the SIR and SEIR epidemiological models with two time-varying parameters that capture the transmission rate and the rate at which active cases are reported to health officials. Using two real data sets of COVID-19 cases, we perform Bayesian inference via our SIR and SEIR models with time-varying transmission and reporting rates and via their standard counterparts with constant rates; our approach provides parameter estimates with more realistic interpretation, and 1-week ahead predictions with reduced uncertainty. Furthermore, we find consistent under-reporting in the number of active cases in the data that we consider, suggesting that the initial phase of the pandemic was more widespread than previously reported.

An analysis of COVID-19 spread based on fractal interpolation and fractal dimension

The present paper proposes a reconstruction of the epidemic curves from the fractal interpolation point of view. Looking at the epidemic curves as fractal structures might be an efficient way to retrieve missing pieces of information due to insufficient testing and predict the evolution of the disease. A fractal approach of the epidemic curve can contribute to the assessment and modeling of other epidemics. On the other hand, we have considered the spread of the epidemic in countries like Romania, Italy, Spain, and Germany and analyzed the spread of the disease in those countries based on their fractal dimension.

Influencing public health policy with data-informed mathematical models of infectious diseases: Recent developments and new challenges

Modern data and computational resources, coupled with algorithmic and theoretical advances to exploit these, allow disease dynamic models to be parameterised with increasing detail and accuracy. While this enhances models' usefulness in prediction and policy, major challenges remain. In particular, lack of identifiability of a model's parameters may limit the usefulness of the model. While lack of parameter identifiability may be resolved through incorporation into an inference procedure of prior knowledge, formulating such knowledge is often difficult. Furthermore, there are practical challenges associated with acquiring data of sufficient quantity and quality. Here, we discuss recent progress on these issues.

Mathematical modelling on diffusion and control of COVID-19

In this paper, we develop a mathematical model for the spread and control of the coronavirus disease. An outbreak of COVID-19 has led to more than one million confirmed cases as of April 3rd, 2020. Understanding the early spread dynamics of the infection and evaluating the effectiveness of control measures is crucial for assessing the potential for sustained transmission to occur in new areas. Combining a mathematical model of severe COVID-19 spread with four datasets from within and outside of Wuhan, China; it is estimated how spread in Wuhan varied between January and February 2020. It is used these estimates to assess the potential for sustained human-to-human spread to occur in locations outside Wuhan if disease holders were introduced. It is combined SEIR framework model with data on cases of COVID-19 in China and International cases that originated in Wuhan to estimate how spread had varied over time during January and February 2020. Based on these estimates, it is calculated the probability that freshly introduced cases might produce outbreaks in other regions. Also, it is calculated approximately the median day by day basic reproduction number in Wuhan, refused from 2·45 (95% CI: 1·16-4·87) one week before travel restrictions were introduced on Jan 23rd, 2020, to 1.05 (0·42-2·40) one week after. Based on our estimates of, presumptuous SARS approximating disparity, it is computed that in locations with a similar spread potential to Wuhan in near the beginning of January, some time ago there are at least four independently set up cases, there is a more than fifty percent chance the infection will found within those inhabitants. COVID-19 spreading probably refused in Wuhan during delayed January 2020, corresponding with the prologue of voyage control channels. As more cases arrive in international locations with similar spread potential to Wuhan, before these organize measures, it is likely many chains of spread will fail to create initially but might lead to innovative outbreaks ultimately.

Early dynamics of transmission and control of COVID-19: a mathematical modelling study

BACKGROUND

An outbreak of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has led to 95 333 confirmed cases as of March 5, 2020. Understanding the early transmission dynamics of the infection and evaluating the effectiveness of control measures is crucial for assessing the potential for sustained transmission to occur in new areas. Combining a mathematical model of severe SARS-CoV-2 transmission with four datasets from within and outside Wuhan, we estimated how transmission in Wuhan varied between December, 2019, and February, 2020. We used these estimates to assess the potential for sustained human-to-human transmission to occur in locations outside Wuhan if cases were introduced.

METHODS

We combined a stochastic transmission model with data on cases of coronavirus disease 2019 (COVID-19) in Wuhan and international cases that originated in Wuhan to estimate how transmission had varied over time during January, 2020, and February, 2020. Based on these estimates, we then calculated the probability that newly introduced cases might generate outbreaks in other areas. To estimate the early dynamics of transmission in Wuhan, we fitted a stochastic transmission dynamic model to multiple publicly available datasets on cases in Wuhan and internationally exported cases from Wuhan. The four datasets we fitted to were: daily number of new internationally exported cases (or lack thereof), by date of onset, as of Jan 26, 2020; daily number of new cases in Wuhan with no market exposure, by date of onset, between Dec 1, 2019, and Jan 1, 2020; daily number of new cases in China, by date of onset, between Dec 29, 2019, and Jan 23, 2020; and proportion of infected passengers on evacuation flights between Jan 29, 2020, and Feb 4, 2020. We used an additional two datasets for comparison with model outputs: daily number of new exported cases from Wuhan (or lack thereof) in countries with high connectivity to Wuhan (ie, top 20 most at-risk countries), by date of confirmation, as of Feb 10, 2020; and data on new confirmed cases reported in Wuhan between Jan 16, 2020, and Feb 11, 2020.

FINDINGS

We estimated that the median daily reproduction number (R_t) in Wuhan declined from 2·35 (95% CI 1·15-4·77) 1 week before travel restrictions were introduced on Jan 23, 2020, to 1·05 (0·41-2·39) 1 week after. Based on our estimates of R_t, assuming SARS-like variation, we calculated that in locations with similar transmission potential to Wuhan in early January, once there are at least four independently introduced cases, there is a more than 50% chance the infection will establish within that population.

INTERPRETATION

Our results show that COVID-19 transmission probably declined in Wuhan during late January, 2020, coinciding with the introduction of travel control measures. As more cases arrive in international locations with similar transmission potential to Wuhan before these control measures, it is likely many chains of transmission will fail to establish initially, but might lead to new outbreaks eventually.

FUNDING

Wellcome Trust, Health Data Research UK, Bill & Melinda Gates Foundation, and National Institute for Health Research.

Early dynamics of transmission and control of COVID-19: a mathematical modelling study

BACKGROUND

An outbreak of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has led to 95 333 confirmed cases as of March 5, 2020. Understanding the early transmission dynamics of the infection and evaluating the effectiveness of control measures is crucial for assessing the potential for sustained transmission to occur in new areas. Combining a mathematical model of severe SARS-CoV-2 transmission with four datasets from within and outside Wuhan, we estimated how transmission in Wuhan varied between December, 2019, and February, 2020. We used these estimates to assess the potential for sustained human-to-human transmission to occur in locations outside Wuhan if cases were introduced.

METHODS

We combined a stochastic transmission model with data on cases of coronavirus disease 2019 (COVID-19) in Wuhan and international cases that originated in Wuhan to estimate how transmission had varied over time during January, 2020, and February, 2020. Based on these estimates, we then calculated the probability that newly introduced cases might generate outbreaks in other areas. To estimate the early dynamics of transmission in Wuhan, we fitted a stochastic transmission dynamic model to multiple publicly available datasets on cases in Wuhan and internationally exported cases from Wuhan. The four datasets we fitted to were: daily number of new internationally exported cases (or lack thereof), by date of onset, as of Jan 26, 2020; daily number of new cases in Wuhan with no market exposure, by date of onset, between Dec 1, 2019, and Jan 1, 2020; daily number of new cases in China, by date of onset, between Dec 29, 2019, and Jan 23, 2020; and proportion of infected passengers on evacuation flights between Jan 29, 2020, and Feb 4, 2020. We used an additional two datasets for comparison with model outputs: daily number of new exported cases from Wuhan (or lack thereof) in countries with high connectivity to Wuhan (ie, top 20 most at-risk countries), by date of confirmation, as of Feb 10, 2020; and data on new confirmed cases reported in Wuhan between Jan 16, 2020, and Feb 11, 2020.

FINDINGS

We estimated that the median daily reproduction number (Rt) in Wuhan declined from 2·35 (95% CI 1·15-4·77) 1 week before travel restrictions were introduced on Jan 23, 2020, to 1·05 (0·41-2·39) 1 week after. Based on our estimates of Rt, assuming SARS-like variation, we calculated that in locations with similar transmission potential to Wuhan in early January, once there are at least four independently introduced cases, there is a more than 50% chance the infection will establish within that population.

INTERPRETATION

Our results show that COVID-19 transmission probably declined in Wuhan during late January, 2020, coinciding with the introduction of travel control measures. As more cases arrive in international locations with similar transmission potential to Wuhan before these control measures, it is likely many chains of transmission will fail to establish initially, but might lead to new outbreaks eventually.

FUNDING

Wellcome Trust, Health Data Research UK, Bill & Melinda Gates Foundation, and National Institute for Health Research.

Early dynamics of transmission and control of COVID-19: a mathematical modelling study

BACKGROUND

An outbreak of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has led to 95 333 confirmed cases as of March 5, 2020. Understanding the early transmission dynamics of the infection and evaluating the effectiveness of control measures is crucial for assessing the potential for sustained transmission to occur in new areas. Combining a mathematical model of severe SARS-CoV-2 transmission with four datasets from within and outside Wuhan, we estimated how transmission in Wuhan varied between December, 2019, and February, 2020. We used these estimates to assess the potential for sustained human-to-human transmission to occur in locations outside Wuhan if cases were introduced.

METHODS

We combined a stochastic transmission model with data on cases of coronavirus disease 2019 (COVID-19) in Wuhan and international cases that originated in Wuhan to estimate how transmission had varied over time during January, 2020, and February, 2020. Based on these estimates, we then calculated the probability that newly introduced cases might generate outbreaks in other areas. To estimate the early dynamics of transmission in Wuhan, we fitted a stochastic transmission dynamic model to multiple publicly available datasets on cases in Wuhan and internationally exported cases from Wuhan. The four datasets we fitted to were: daily number of new internationally exported cases (or lack thereof), by date of onset, as of Jan 26, 2020; daily number of new cases in Wuhan with no market exposure, by date of onset, between Dec 1, 2019, and Jan 1, 2020; daily number of new cases in China, by date of onset, between Dec 29, 2019, and Jan 23, 2020; and proportion of infected passengers on evacuation flights between Jan 29, 2020, and Feb 4, 2020. We used an additional two datasets for comparison with model outputs: daily number of new exported cases from Wuhan (or lack thereof) in countries with high connectivity to Wuhan (ie, top 20 most at-risk countries), by date of confirmation, as of Feb 10, 2020; and data on new confirmed cases reported in Wuhan between Jan 16, 2020, and Feb 11, 2020.

FINDINGS

We estimated that the median daily reproduction number (R_t) in Wuhan declined from 2·35 (95% CI 1·15-4·77) 1 week before travel restrictions were introduced on Jan 23, 2020, to 1·05 (0·41-2·39) 1 week after. Based on our estimates of R_t, assuming SARS-like variation, we calculated that in locations with similar transmission potential to Wuhan in early January, once there are at least four independently introduced cases, there is a more than 50% chance the infection will establish within that population.

INTERPRETATION

Our results show that COVID-19 transmission probably declined in Wuhan during late January, 2020, coinciding with the introduction of travel control measures. As more cases arrive in international locations with similar transmission potential to Wuhan before these control measures, it is likely many chains of transmission will fail to establish initially, but might lead to new outbreaks eventually.

FUNDING

Wellcome Trust, Health Data Research UK, Bill & Melinda Gates Foundation, and National Institute for Health Research.

Outbreak analytics: a developing data science for informing the response to emerging pathogens

Despite continued efforts to improve health systems worldwide, emerging pathogen epidemics remain a major public health concern. Effective response to such outbreaks relies on timely intervention, ideally informed by all available sources of data. The collection, visualization and analysis of outbreak data are becoming increasingly complex, owing to the diversity in types of data, questions and available methods to address them. Recent advances have led to the rise of outbreak analytics, an emerging data science focused on the technological and methodological aspects of the outbreak data pipeline, from collection to analysis, modelling and reporting to inform outbreak response. In this article, we assess the current state of the field. After laying out the context of outbreak response, we critically review the most common analytics components, their inter-dependencies, data requirements and the type of information they can provide to inform operations in real time. We discuss some challenges and opportunities and conclude on the potential role of outbreak analytics for improving our understanding of, and response to outbreaks of emerging pathogens. 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'.

Anatomy of a seasonal influenza epidemic forecast

Bayesian methods have been used to predict the timing of infectious disease epidemics in various settings and for many infectious diseases, including seasonal influenza. But integrating these techniques into public health practice remains an ongoing challenge, and requires close collaboration between modellers, epidemiologists, and public health staff. During the 2016 and 2017 Australian influenza seasons, weekly seasonal influenza forecasts were produced for cities in the three states with the largest populations: Victoria, New South Wales, and Queensland. Forecast results were presented to Health Department disease surveillance units in these jurisdictions, who provided feedback about the plausibility and public health utility of these predictions. In earlier studies we found that delays in reporting and processing of surveillance data substantially limited forecast performance, and that incorporating climatic effects on transmission improved forecast performance. In this study of the 2016 and 2017 seasons, we sought to refine the forecasting method to account for delays in receiving the data, and used meteorological data from past years to modulate the force of infection. We demonstrate how these refinements improved the forecast’s predictive capacity, and use the 2017 influenza season to highlight challenges in accounting for population and clinician behaviour changes in response to a severe season.

Accounting for Healthcare-Seeking Behaviours and Testing Practices in Real-Time Influenza Forecasts

For diseases such as influenza, where the majority of infected persons experience mild (if any) symptoms, surveillance systems are sensitive to changes in healthcare-seeking and clinical decision-making behaviours. This presents a challenge when trying to interpret surveillance data in near-real-time (e.g., to provide public health decision-support). Australia experienced a particularly large and severe influenza season in 2017, perhaps in part due to: (a) mild cases being more likely to seek healthcare; and (b) clinicians being more likely to collect specimens for reverse transcription polymerase chain reaction (RT-PCR) influenza tests. In this study, we used weekly Flutracking surveillance data to estimate the probability that a person with influenza-like illness (ILI) would seek healthcare and have a specimen collected. We then used this estimated probability to calibrate near-real-time seasonal influenza forecasts at each week of the 2017 season, to see whether predictive skill could be improved. While the number of self-reported influenza tests in the weekly surveys are typically very low, we were able to detect a substantial change in healthcare seeking behaviour and clinician testing behaviour prior to the high epidemic peak. Adjusting for these changes in behaviour in the forecasting framework improved predictive skill. Our analysis demonstrates a unique value of community-level surveillance systems, such as Flutracking, when interpreting traditional surveillance data. These methods are also applicable beyond the Australian context, as similar community-level surveillance systems operate in other countries.

A Bayesian evidence synthesis approach to estimate disease prevalence in hard-to-reach populations: hepatitis C in New York City

Existing methods to estimate the prevalence of chronic hepatitis C (HCV) in New York City (NYC) are limited in scope and fail to assess hard-to-reach subpopulations with highest risk such as injecting drug users (IDUs). To address these limitations, we employ a Bayesian multi-parameter evidence synthesis model to systematically combine multiple sources of data, account for bias in certain data sources, and provide unbiased HCV prevalence estimates with associated uncertainty. Our approach improves on previous estimates by explicitly accounting for injecting drug use and including data from high-risk subpopulations such as the incarcerated, and is more inclusive, utilizing ten NYC data sources. In addition, we derive two new equations to allow age at first injecting drug use data for former and current IDUs to be incorporated into the Bayesian evidence synthesis, a first for this type of model. Our estimated overall HCV prevalence as of 2012 among NYC adults aged 20-59 years is 2.78% (95% CI 2.61-2.94%), which represents between 124,900 and 140,000 chronic HCV cases. These estimates suggest that HCV prevalence in NYC is higher than previously indicated from household surveys (2.2%) and the surveillance system (2.37%), and that HCV transmission is increasing among young injecting adults in NYC. An ancillary benefit from our results is an estimate of current IDUs aged 20-59 in NYC: 0.58% or 27,600 individuals.