A Bayesian predictive analytics model for improving long range epidemic forecasting during an infection wave

Following the outbreak of the coronavirus epidemic in early 2020, municipalities, regional governments and policymakers worldwide had to plan their Non-Pharmaceutical Interventions (NPIs) amidst a scenario of great uncertainty. At this early stage of an epidemic, where no vaccine or medical treatment is in sight, algorithmic prediction can become a powerful tool to inform local policymaking. However, when we replicated one prominent epidemiological model to inform health authorities in a region in the south of Brazil, we found that this model relied too heavily on manually predetermined covariates and was too reactive to changes in data trends. Our four proposed models access data of both daily reported deaths and infections as well as take into account missing data (e.g., the under-reporting of cases) more explicitly, with two of the proposed versions also attempting to model the delay in test reporting. We simulated weekly forecasting of deaths from the period from 31/05/2020 until 31/01/2021, with first week data being used as a cold-start to the algorithm, after which we use a lighter variant of the model for faster forecasting. Because our models are significantly more proactive in identifying trend changes, this has improved forecasting, especially in long-range predictions and after the peak of an infection wave, as they were quicker to adapt to scenarios after these peaks in reported deaths. Assuming reported cases were under-reported greatly benefited the model in its stability, and modelling retroactively-added data (due to the "hot" nature of the data used) had a negligible impact on performance.

Sequential time-window learning with approximate Bayesian computation: an application to epidemic forecasting

The long duration of the COVID-19 pandemic allowed for multiple bursts in the infection and death rates, the so-called epidemic waves. This complex behavior is no longer tractable by simple compartmental model and requires more sophisticated mathematical techniques for analyzing epidemic data and generating reliable forecasts. In this work, we propose a framework for analyzing complex dynamical systems by dividing the data in consecutive time-windows to be separately analyzed. We fit parameters for each time-window through an approximate Bayesian computation (ABC) algorithm, and the posterior distribution of parameters obtained for one window is used as the prior distribution for the next window. This Bayesian learning approach is tested with data on COVID-19 cases in multiple countries and is shown to improve ABC performance and to produce good short-term forecasting.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s11071-022-07865-x.

Forecasting new diseases in low-data settings using transfer learning

Recent infectious disease outbreaks, such as the COVID-19 pandemic and the Zika epidemic in Brazil, have demonstrated both the importance and difficulty of accurately forecasting novel infectious diseases. When new diseases first emerge, we have little knowledge of the transmission process, the level and duration of immunity to reinfection, or other parameters required to build realistic epidemiological models. Time series forecasts and machine learning, while less reliant on assumptions about the disease, require large amounts of data that are also not available in early stages of an outbreak. In this study, we examine how knowledge of related diseases can help make predictions of new diseases in data-scarce environments using transfer learning. We implement both an empirical and a synthetic approach. Using data from Brazil, we compare how well different machine learning models transfer knowledge between two different dataset pairs: case counts of (i) dengue and Zika, and (ii) influenza and COVID-19. In the synthetic analysis, we generate data with an SIR model using different transmission and recovery rates, and then compare the effectiveness of different transfer learning methods. We find that transfer learning offers the potential to improve predictions, even beyond a model based on data from the target disease, though the appropriate source disease must be chosen carefully. While imperfect, these models offer an additional input for decision makers for pandemic response.

Analysis and prediction of COVID-19 epidemic in South Africa

The coronavirus disease-2019 (COVID-19) has been spreading rapidly in South Africa (SA) since its first case on 5 March 2020. In total, 674,339 confirmed cases and 16,734 mortality cases were reported by 30 September 2020, and this pandemic has made severe impacts on economy and life. In this paper, analysis and long-term prediction of the epidemic dynamics of SA are made, which could assist the government and public in assessing the past Infection Prevention and Control Measures and designing the future ones to contain the epidemic more effectively. A Susceptible-Infectious-Recovered model is adopted to analyse epidemic dynamics. The model parameters are estimated over different phases with the SA data. They indicate variations in the transmissibility of COVID-19 under different phases and thus reveal weakness of the past Infection Prevention and Control Measures in SA. The model also shows that transient behaviours of the daily growth rate and the cumulative removal rate exhibit periodic oscillations. Such dynamics indicates that the underlying signals are not stationary and conventional linear and nonlinear models would fail for long-term prediction. Therefore, a large class of mappings with rich functions and operations is chosen as the model class and the evolutionary algorithm is utilized to obtain the optimal model for long term prediction. The resulting models on the daily growth rate, the cumulative removal rate and the cumulative mortality rate predict that the peak and inflection point will occur on November 4, 2020 and October 15, 2020, respectively; the virus shall cease spreading on April 28, 2021; and the ultimate numbers of the COVID-19 cases and mortality cases will be 785,529 and 17,072, respectively. The approach is also benchmarked against other methods and shows better accuracy of long-term prediction.

A simple mathematical tool to forecast COVID-19 cumulative case numbers

Objective

Mathematical models are known to help determine potential intervention strategies by providing an approximate idea of the transmission dynamics of infectious diseases. To develop proper responses, not only are more accurate disease spread models needed, but also those that are easy to use.

Materials and methods

As of July 1, 2020, we selected the 20 countries with the highest numbers of COVID-19 cases in the world. Using the Verhulst–Pearl logistic function formula, we calculated estimates for the total number of cases for each country. We compared these estimates to the actual figures given by the WHO on the same dates. Finally, the formula was tested for longer-term reliability at t = 18 and t = 40 weeks.

Results

The Verhulst–Pearl logistic function formula estimated the actual numbers precisely, with only a 0.5% discrepancy on average for the first month. For all countries in the study and the world at large, the estimates for the 40th week were usually overestimated, although the estimates for some countries were still relatively close to the actual numbers in the forecasting long term. The estimated number for the world in general was about 8 times that actually observed for the long term.

Conclusions

The Verhulst–Pearl equation has the advantage of being very straightforward and applicable in clinical use for predicting the demand on hospitals in the short term of 4–6 weeks, which is usually enough time to reschedule elective procedures and free beds for new waves of the pandemic patients.

Forecasting the impact of environmental stresses on the frequent waves of COVID19

A novel approach to link the environmental stresses with the COVID-19 cases is adopted during this research. The time-dependent data are extracted from the online repositories that are freely available for knowledge and research. Since the time series data analysis is desired for the COVID-19 time-dependent frequent waves, here in this manuscript, we have developed a time series model with the aid of "nonlinear autoregressive network with exogenous inputs (NARX)" approach. The distribution of infectious agent-containing droplets from an infected person to an uninfected person is a common form of respiratory disease transmission. SARS-CoV-2 has mainly spread via short-range respiratory droplet transmission. Airborne transmission of SARS-CoV-2 seems to have occurred over long distances or times in unusual conditions; SARS-CoV-2 RNA was found in PM10 collected in Italy. This research shows that SARS-CoV-2 particles adsorbed to outdoor PM remained viable for a long time, given the epidemiology of COVID-19, outdoor air pollution is unlikely to be a significant route of transmission. In this research, ANN time series is used to analyze the data resulting from the COVID-19 first and second waves and the forecasted results show that air pollution affects people in different areas of Italy and make more people sick with covid-19. The model is developed based on the disease transmission data of Italy.

[Fitting and forecasting the trend of COVID-19 by SEIR(+CAQ) dynamic model]

Objectives: Fitting and forecasting the trend of COVID-19 epidemics. Methods: Based on SEIR dynamic model, considering the COVID-19 transmission mechanism, infection spectrum and prevention and control procedures, we developed SEIR(+CAQ) dynamic model to fit the frequencies of laboratory confirmed cases obtained from the government official websites. The data from January 20, 2020 to February 7, 2020 were used to fit the model, while the left data between February 8-12 were used to evaluate the quality of forecasting. Results: According to the cumulative number of confirmed cases between January 29 to February 7, the fitting bias of SEIR(+CAQ) model for overall China (except for cases of Hubei province), Hubei province (except for cases of Wuhan city) and Wuhan city was less than 5%. For the data of subsequent 5 days between February 8 to 12, which were not included in the model fitting, the prediction biases were less than 10%. Regardless of the cases diagnosed by clinical examines, the numbers of daily emerging cases of China (Hubei province not included), Hubei Province (Wuhan city not included) and Wuhan city reached the peak in the early February. Under the current strength of prevention and control, the total number of laboratory-confirmed cases in overall China will reach 80 417 till February 29, 2020, respectively. Conclusions: The proposed SEIR(+CAQ) dynamic model fits and forecasts the trend of novel coronavirus pneumonia well and provides evidence for decision making.

Real-time forecasting of epidemic trajectories using computational dynamic ensembles

Forecasting the trajectory of social dynamic processes, such as the spread of infectious diseases, poses significant challenges that call for methods that account for data and model uncertainty. Here we introduce an ensemble model for sequential forecasting that weights a set of plausible models and use a frequentist computational bootstrap approach to evaluate its uncertainty. We demonstrate the feasibility of our approach using simple dynamic differential-equation models and the trajectory of outbreak scenarios of the Ebola Forecasting Challenge. Specifically, we generate sequential short-term forecasts of epidemic outbreaks by combining phenomenological models that incorporate flexible epidemic growth scaling, namely the Generalized-Growth Model (GGM) and the Generalized Logistic Model (GLM). We rely on the root-mean-square error (RMSE) to quantify the quality of the models' fits during the calibration periods for weighting their contribution to the ensemble model while forecasting performance was evaluated using the RMSE of the forecasts. For a given forecasting horizon (1-4 weeks), we report the performance for each model as the percentage of the number of times each model outperforms the other models. The overall mean RMSE performance of the GLM and the GGM-GLM ensemble models outcompeted that of participant models of the Ebola Forecasting Challenge. We also found that the ensemble model provided more accurate forecasts with higher frequency than the GGM and GLM models, but its performance varied across forecasting horizons. For instance, across all of the Ebola Challenge Scenarios, the ensemble model outperformed the other models at horizons of 2 and 3 weeks while the GLM outperformed other models at horizons of 1 and 4 weeks.

Accurate forecasts of the effectiveness of interventions against Ebola may require models that account for variations in symptoms during infection

Epidemiological models are routinely used to predict the effects of interventions aimed at reducing the impacts of Ebola epidemics. Most models of interventions targeting symptomatic hosts, such as isolation or treatment, assume that all symptomatic hosts are equally likely to be detected. In other words, following an incubation period, the level of symptoms displayed by an individual host is assumed to remain constant throughout an infection. In reality, however, symptoms vary between different stages of infection. During an Ebola infection, individuals progress from initial non-specific symptoms through to more severe phases of infection. Here we compare predictions of a model in which a constant symptoms level is assumed to those generated by a more epidemiologically realistic model that accounts for varying symptoms during infection. Both models can reproduce observed epidemic data, as we show by fitting the models to data from the ongoing epidemic in the Democratic Republic of the Congo and the 2014-16 epidemic in Liberia. However, for both of these epidemics, when interventions are altered identically in the models with and without levels of symptoms that depend on the time since first infection, predictions from the models differ. Our work highlights the need to consider whether or not varying symptoms should be accounted for in models used by decision makers to assess the likely efficacy of Ebola interventions.

A primer on stable parameter estimation and forecasting in epidemiology by a problem-oriented regularized least squares algorithm

Public health officials are increasingly recognizing the need to develop disease-forecasting systems to respond to epidemic and pandemic outbreaks. For instance, simple epidemic models relying on a small number of parameters can play an important role in characterizing epidemic growth and generating short-term epidemic forecasts. In the absence of reliable information about transmission mechanisms of emerging infectious diseases, phenomenological models are useful to characterize epidemic growth patterns without the need to explicitly model transmission mechanisms and the natural history of the disease. In this article, our goal is to discuss and illustrate the role of regularization methods for estimating parameters and generating disease forecasts using the generalized Richards model in the context of the 2014–15 Ebola epidemic in West Africa.

A framework for evaluating epidemic forecasts

Background

Over the past few decades, numerous forecasting methods have been proposed in the field of epidemic forecasting. Such methods can be classified into different categories such as deterministic vs. probabilistic, comparative methods vs. generative methods, and so on. In some of the more popular comparative methods, researchers compare observed epidemiological data from the early stages of an outbreak with the output of proposed models to forecast the future trend and prevalence of the pandemic. A significant problem in this area is the lack of standard well-defined evaluation measures to select the best algorithm among different ones, as well as for selecting the best possible configuration for a particular algorithm.

Results

In this paper we present an evaluation framework which allows for combining different features, error measures, and ranking schema to evaluate forecasts. We describe the various epidemic features (Epi-features) included to characterize the output of forecasting methods and provide suitable error measures that could be used to evaluate the accuracy of the methods with respect to these Epi-features. We focus on long-term predictions rather than short-term forecasting and demonstrate the utility of the framework by evaluating six forecasting methods for predicting influenza in the United States. Our results demonstrate that different error measures lead to different rankings even for a single Epi-feature. Further, our experimental analyses show that no single method dominates the rest in predicting all Epi-features when evaluated across error measures. As an alternative, we provide various Consensus Ranking schema that summarize individual rankings, thus accounting for different error measures. Since each Epi-feature presents a different aspect of the epidemic, multiple methods need to be combined to provide a comprehensive forecast. Thus we call for a more nuanced approach while evaluating epidemic forecasts and we believe that a comprehensive evaluation framework, as presented in this paper, will add value to the computational epidemiology community.

Electronic supplementary material

The online version of this article (doi:10.1186/s12879-017-2365-1) contains supplementary material, which is available to authorized users.