Data-driven outbreak forecasting with a simple nonlinear growth model

GrowthPredict: A toolbox and tutorial-based primer for fitting and forecasting growth trajectories using phenomenological growth models

Simple dynamic modeling tools can help generate real-time short-term forecasts with quantified uncertainty of the trajectory of diverse growth processes unfolding in nature and society, including disease outbreaks. An easy-to-use and flexible toolbox for this purpose is lacking. This tutorial-based primer introduces and illustrates GrowthPredict, a user-friendly MATLAB toolbox for fitting and forecasting time-series trajectories using phenomenological dynamic growth models based on ordinary differential equations. This toolbox is accessible to a broad audience, including students training in mathematical biology, applied statistics, and infectious disease modeling, as well as researchers and policymakers who need to conduct short-term forecasts in real-time. The models included in the toolbox capture exponential and sub-exponential growth patterns that typically follow a rising pattern followed by a decline phase, a common feature of contagion processes. Models include the 1-parameter exponential growth model and the 2-parameter generalized-growth model, which have proven useful in characterizing and forecasting the ascending phase of epidemic outbreaks. It also includes the 2-parameter Gompertz model, the 3-parameter generalized logistic-growth model, and the 3-parameter Richards model, which have demonstrated competitive performance in forecasting single peak outbreaks. We provide detailed guidance on forecasting time-series trajectories and available software ( https://github.com/gchowell/forecasting_growthmodels ), including the full uncertainty distribution derived through parametric bootstrapping, which is needed to construct prediction intervals and evaluate their accuracy. Functions are available to assess forecasting performance across different models, estimation methods, error structures in the data, and forecasting horizons. The toolbox also includes functions to quantify forecasting performance using metrics that evaluate point and distributional forecasts, including the weighted interval score. This tutorial and toolbox can be broadly applied to characterizing and forecasting time-series data using simple phenomenological growth models. As a contagion process takes off, the tools presented in this tutorial can help create forecasts to guide policy regarding implementing control strategies and assess the impact of interventions. The toolbox functionality is demonstrated through various examples, including a tutorial video, and the examples use publicly available data on the monkeypox (mpox) epidemic in the USA.

Fitting Early Phases of the COVID-19 Outbreak: A Comparison of the Performances of Used Models

The COVID-19 outbreak involved a spread of prediction efforts, especially in the early pandemic phase. A better understanding of the epidemiological implications of the different models seems crucial for tailoring prevention policies. This study aims to explore the concordance and discrepancies in outbreak prediction produced by models implemented and used in the first wave of the epidemic. To evaluate the performance of the model, an analysis was carried out on Italian pandemic data from February 24, 2020. The epidemic models were fitted to data collected at 20, 30, 40, 50, 60, 70, 80, 90, and 98 days (the entire time series). At each time step, we made predictions until May 31, 2020. The Mean Absolute Error (MAE) and the Mean Absolute Percentage Error (MAPE) were calculated. The GAM model is the most suitable parameterization for predicting the number of new cases; exponential or Poisson models help predict the cumulative number of cases. When the goal is to predict the epidemic peak, GAM, ARIMA, or Bayesian models are preferable. However, the prediction of the pandemic peak could be made carefully during the early stages of the epidemic because the forecast is affected by high uncertainty and may very likely produce the wrong results.

A MATLAB toolbox to fit and forecast growth trajectories using phenomenological growth models: Application to epidemic outbreaks

BACKGROUND

Simple dynamic modeling tools can be useful for generating real-time short-term forecasts with quantified uncertainty of the trajectory of diverse growth processes unfolding in nature and society, including disease outbreaks. An easy-to-use and flexible toolbox for this purpose is lacking.

RESULTS

In this tutorial-based primer, we introduce and illustrate a user-friendly MATLAB toolbox for fitting and forecasting time-series trajectories using phenomenological dynamic growth models based on ordinary differential equations. This toolbox is accessible to various audiences, including students training in time-series forecasting, dynamic growth modeling, parameter estimation, parameter uncertainty and identifiability, model comparison, performance metrics, and forecast evaluation, as well as researchers and policymakers who need to conduct short-term forecasts in real-time. The models included in the toolbox capture exponential and sub-exponential growth patterns that typically follow a rising pattern followed by a decline phase, a common feature of contagion processes. Models include the 2-parameter generalized-growth model, which has proved useful to characterize and forecast the ascending phase of epidemic outbreaks, and the Gompertz model as well as the 3-parameter generalized logistic-growth model and the Richards model, which have demonstrated competitive performance in forecasting single peak outbreaks.The toolbox provides a tutorial for forecasting time-series trajectories that include the full uncertainty distribution, derived through parametric bootstrapping, which is needed to construct prediction intervals and evaluate their accuracy. Functions are available to assess forecasting performance across different models, estimation methods, error structures in the data, and forecasting horizons. The toolbox also includes functions to quantify forecasting performance using metrics that evaluate point and distributional forecasts, including the weighted interval score.

CONCLUSIONS

We have developed the first comprehensive toolbox to characterize and forecast time-series data using simple phenomenological growth models. As a contagion process takes off, the tools presented in this tutorial can facilitate policymaking to guide the implementation of control strategies and assess the impact of interventions. The toolbox functionality is demonstrated through various examples, including a tutorial video, and is illustrated using weekly data on the monkeypox epidemic in the USA.

Usage of Compartmental Models in Predicting COVID-19 Outbreaks

Accurately predicting the spread of the SARS-CoV-2, the cause of the COVID-19 pandemic, is of great value for global regulatory authorities to overcome a number of challenges including medication shortage, outcome of vaccination, and control strategies planning. Modeling methods that are used to simulate and predict the spread of COVID-19 include compartmental model, structured metapopulations, agent-based networks, deep learning, and complex network, with compartmental modeling as one of the most widely used methods. Compartmental model has two noteworthy features, a flexible framework that allows users to easily customize the model structure and its high adaptivity that allows well-matured approaches (e.g., Bayesian inference and mixed-effects modeling) to improve parameter estimation. We retrospectively evaluated the prediction performances of the compartmental models on the CDC COVID-19 Mathematical Modeling webpage based on data collected between August 2020 and February 2021, and subsequently discussed in detail their corresponding model enhancement. Finally, we presented examples using the compartmental models to assist policymaking. By evaluating all models in parallel, we systemically evaluated the performance and evolution of using compartmental models for COVID-19 pandemic prediction. In summary, as a 100-year-old epidemic approach, the compartmental model presents a powerful tool that is extremely adaptive and can be readily customized and implemented to address new data or emerging needs during a pandemic.

Comparing trained and untrained probabilistic ensemble forecasts of COVID-19 cases and deaths in the United States

The U.S. COVID-19 Forecast Hub aggregates forecasts of the short-term burden of COVID-19 in the United States from many contributing teams. We study methods for building an ensemble that combines forecasts from these teams. These experiments have informed the ensemble methods used by the Hub. To be most useful to policy makers, ensemble forecasts must have stable performance in the presence of two key characteristics of the component forecasts: (1) occasional misalignment with the reported data, and (2) instability in the relative performance of component forecasters over time. Our results indicate that in the presence of these challenges, an untrained and robust approach to ensembling using an equally weighted median of all component forecasts is a good choice to support public health decision makers. In settings where some contributing forecasters have a stable record of good performance, trained ensembles that give those forecasters higher weight can also be helpful.

Parameter estimation from ICC curves

Incidence vs. Cumulative Cases (ICC) curves are introduced and shown to provide a simple framework for parameter identification in the case of the most elementary epidemiological model, consisting of susceptible, infected, and removed compartments. This novel methodology is used to estimate the basic reproduction ratio of recent outbreaks, including those associated with the ongoing COVID-19 pandemic.

Emergence of universality in the transmission dynamics of COVID-19

The complexities involved in modelling the transmission dynamics of COVID-19 has been a roadblock in achieving predictability in the spread and containment of the disease. In addition to understanding the modes of transmission, the effectiveness of the mitigation methods also needs to be built into any effective model for making such predictions. We show that such complexities can be circumvented by appealing to scaling principles which lead to the emergence of universality in the transmission dynamics of the disease. The ensuing data collapse renders the transmission dynamics largely independent of geopolitical variations, the effectiveness of various mitigation strategies, population demographics, etc. We propose a simple two-parameter model-the Blue Sky model-and show that one class of transmission dynamics can be explained by a solution that lives at the edge of a blue sky bifurcation. In addition, the data collapse leads to an enhanced degree of predictability in the disease spread for several geographical scales which can also be realized in a model-independent manner as we show using a deep neural network. The methodology adopted in this work can potentially be applied to the transmission of other infectious diseases and new universality classes may be found. The predictability in transmission dynamics and the simplicity of our methodology can help in building policies for exit strategies and mitigation methods during a pandemic.

Situation assessment and natural dynamics of COVID-19 pandemic in Nigeria, 31 May 2020

Background

The coronavirus disease (COVID-19) remains a global public health issue due to its high transmission and case fatality rate. There is apprehension on how to curb the spread and mitigate the socio-economic impacts of the pandemic, but timely and reliable daily confirmed cases' estimates are pertinent to the pandemic's containment. This study therefore conducted a situation assessment and applied simple predictive models to explore COVID-19 progression in Nigeria as at 31 May 2020.

Methods

Data used for this study were extracted from the websites of the European Centre for Disease Control (World Bank data) and Nigeria Centre for Disease Control. Besides descriptive statistics, four predictive models were fitted to investigate the pandemic natural dynamics.

Results

The case fatality rate of COVID-19 was 2.8%. A higher number of confirmed cases of COVID-19 was reported daily after the relaxation of lockdown than before and during lockdown. Of the 36 states in Nigeria, including the Federal Capital Territory, 35 have been affected with COVID-19. Most active cases were in Lagos (n = 4064; 59.2%), followed by Kano (n = 669; 9.2%). The percentage of COVID-19 recovery in Nigeria (29.5%) was lower compared to South Africa (50.3%), but higher compared to Kenya (24.1%). The cubic polynomial model had the best fit. The projected value for COVID-19 cumulative cases for 30 June 2020 in Nigeria was 27,993 (95% C.I: 27,001–28,986).

Conclusion

The daily confirmed cases of COVID-19 are increasing in Nigeria. Increasing testing capacity for the disease may further reveal more confirmed cases. As observed in this study, the cubic polynomial model currently offers a better prediction of the future COVID-19 cases in Nigeria.

Three pre-vaccine responses to Covid-like epidemics

This paper contains a theoretical study of epidemic control. It is inspired by current events but not intended to be an accurate depiction of the SARS-CoV-2 pandemic. We consider the emergence of a highly transmissible pathogen, focusing on metropolitan areas. To ensure some degree of realism, we present a conceptual model of the outbreak and early attempts to stave off the onslaught, including the use of lockdowns. Model outputs show strong qualitative—in some respects even quantitative—resemblance to the events of Spring 2020 in many cities worldwide. We then use this model to project forward in time to examine different paths in epidemic control after the initial surge is tamed and before the arrival of vaccines. Three very different control strategies are analyzed, leading to vastly different outcomes in terms of economic recovery and total infected population (or progress toward herd immunity). Our model, which is a version of the SEIQR model, is a time-dependent dynamical system with feedback-control. One of the main conclusions of this analysis is that the course of the epidemic is not entirely dictated by the virus: how the population responds to it can play an equally important role in determining the eventual outcome.

EpiCovDA: a mechanistic COVID-19 forecasting model with data assimilation

We introduce a minimalist outbreak forecasting model that combines data-driven parameter estimation with variational data assimilation. By focusing on the fundamental components of nonlinear disease transmission and representing data in a domain where model stochasticity simplifies into a process with independent increments, we design an approach that only requires four core parameters to be estimated. We illustrate this novel methodology on COVID-19 forecasts. Results include case count and deaths predictions for the US and all of its 50 states, the District of Columbia, and Puerto Rico. The method is computationally efficient and is not disease- or location-specific. It may therefore be applied to other outbreaks or other countries, provided case counts and/or deaths data are available.

Monitoring and forecasting the COVID-19 epidemic in the UK

This paper shows how existing methods of time series analysis and modeling can be exploited in novel ways to monitor and forecast the COVID-19 epidemic. In the past, epidemics have been monitored by various statistical and model metrics, such as evaluation of the effective reproduction number, R ( t ) . However, R ( t ) can be difficult and time consuming to compute. This paper suggests two relatively simple data-based metrics that could be used in conjunction with R ( t ) estimation and provide rapid indicators of how the epidemic's dynamic behavior is progressing. The new metrics are the epidemic rate of change (RC) and a related state-dependent response rate parameter (RP), recursive estimates of which are obtained from dynamic harmonic and dynamic linear regression (DHR and DLR) algorithms. Their effectiveness is illustrated by the analysis of COVID-19 data in the UK and Italy. The paper also shows how similar methodology, combined with the refined instrumental variable method for estimating hybrid Box-Jenkins models of linear dynamic systems (RIVC), can be used to relate the daily death numbers in the Italian and UK epidemics and then provide 15-day-ahead forecasts of the UK daily death numbers. The same approach can be used to model and forecast the UK epidemic based on the daily number of COVID-19 patients in UK hospitals. Finally, the paper speculates on how the state-dependent parameter (SDP) modeling procedures may provide data-based insight into a nonlinear differential equation model for epidemics such as COVID-19.

The behaviour of infection, survival and testing effort variables of SARS-CoV-2: A theoretical modelling based on optimization technique

BACKGROUND

The experiences of SARS-CoV-2 are different in nature among the different states of the world. Studies on survival analysis of such pandemic mainly based on differential equation analysis, but the main limitation of such models is non-universal applicability. Consideration of improper functional relation in case of identification, survival and testing effort variables of the disease may be the cause of such non-universal applicability.

METHODS

Present study using optimization techniques try to find the general functional form for the variables like identification of the carrier's and testing effort. The study uses both the discrete and continuous time procedure of optimization technique. The main objective of the study is to institute relation between the identified carrier's and effort taken for identification.

RESULTS

The study considers test as the pseudo variable for effort of identification. The study found that the relationship between test and identified is not a linear one, rather it is nonlinear quadratic type. The study does not go for using data driven methods to verify the results.

Mycoplasma bovis outbreak in New Zealand cattle: An assessment of transmission trends using surveillance data

Mycoplasma bovis most likely infected New Zealand cattle in the latter half of 2015. Infection was detected in mid-2017 after which control activities were implemented. An official eradication programme commenced in mid-2018, which is ongoing. We examined farm-level tracing and surveillance data to describe the outbreak, analyse transmission trends and make inference on progress towards eradication. Results indicate that cattle movements were the primary means of spread. Although case farms were distributed throughout both islands of New Zealand, most animal movements off infected farms did not result in newly infected farms, indicating Mycoplasma bovis is not highly transmissible between farms. To describe and analyse outbreak trends, we undertook a standard descriptive outbreak investigation, including construction of an epidemic curve and calculation of estimated dissemination ratios. We then employed three empirical models-a non-linear growth model, time series model and branching process model based on time-varying effective reproduction numbers-to further analyse transmission trends and provide short-term forecasts of farm-level incidence. Our analyses suggest that Mycoplasma bovis transmission in New Zealand has declined and progress towards eradication has been made. Few incident cases were forecast for the period between 8 September and 17 December 2019. To date, no case farms with an estimated infection date assigned to this period have been detected; however, case detection is ongoing, and these results need to be interpreted cautiously considering model validation and other important contextual information on performance of the eradication programme, such as the time between infection, detection and implementation of movement controls on case farms.

[Predictive models of the COVID-19 epidemic in Spain with Gompertz curves]

Durante la crisis de salud internacional provocada por la pandemia de COVID-19, además de conocer los datos sobre contagios, muertes y ocupación de camas hospitalarias también es necesario hacer predicciones que ayuden a la gestión de la crisis por parte de las autoridades sanitarias. El presente trabajo tiene como objetivo describir la metodología utilizada para la elaboración de modelos predictivos de contagios y defunciones para la epidemia de COVID-19 en España basados en curvas de Gompertz. La metodología se aplica al total del país y a cada una de sus comunidades autónomas. De acuerdo con los datos oficiales publicados a la fecha de realización de este trabajo, y a través de los modelos descritos, estimamos un total de alrededor de 240.000 contagiados y 25.000 fallecidos al final de la epidemia. Pronosticamos el final de la epidemia entre los meses de junio y julio de 2020.

Discrete time forecasting of epidemics

Forecasting in the domain of infectious diseases aims at estimating the number of cases ahead of time during an epidemic, hence fundamentally requires understanding its dynamics. In fact, estimates about the dynamics help to predict the number of cases in an epidemic, which will depend on determining a few of defining factors such as its starting point, the turning point, growth factor, and the size of the epidemic in total number of cases. In this work a phenomenological model deals with a practical aspect often disregarded in such studies, namely that health surveillance produces counts in batches when aggregated over discrete time, such as days, weeks, months, or other time units. This model enables derivation of equations that permit both estimating key dynamics parameters and forecasting. Results using both severe acute respiratory illness data and synthetic data show that the forecasting follows very well over time the dynamics and is resilient with statistical noise, but has a delay effect due to the discrete time.

An open challenge to advance probabilistic forecasting for dengue epidemics

A wide range of research has promised new tools for forecasting infectious disease dynamics, but little of that research is currently being applied in practice, because tools do not address key public health needs, do not produce probabilistic forecasts, have not been evaluated on external data, or do not provide sufficient forecast skill to be useful. We developed an open collaborative forecasting challenge to assess probabilistic forecasts for seasonal epidemics of dengue, a major global public health problem. Sixteen teams used a variety of methods and data to generate forecasts for 3 epidemiological targets (peak incidence, the week of the peak, and total incidence) over 8 dengue seasons in Iquitos, Peru and San Juan, Puerto Rico. Forecast skill was highly variable across teams and targets. While numerous forecasts showed high skill for midseason situational awareness, early season skill was low, and skill was generally lowest for high incidence seasons, those for which forecasts would be most valuable. A comparison of modeling approaches revealed that average forecast skill was lower for models including biologically meaningful data and mechanisms and that both multimodel and multiteam ensemble forecasts consistently outperformed individual model forecasts. Leveraging these insights, data, and the forecasting framework will be critical to improve forecast skill and the application of forecasts in real time for epidemic preparedness and response. Moreover, key components of this project-integration with public health needs, a common forecasting framework, shared and standardized data, and open participation-can help advance infectious disease forecasting beyond dengue.

Collaborative efforts to forecast seasonal influenza in the United States, 2015-2016

Since 2013, the Centers for Disease Control and Prevention (CDC) has hosted an annual influenza season forecasting challenge. The 2015–2016 challenge consisted of weekly probabilistic forecasts of multiple targets, including fourteen models submitted by eleven teams. Forecast skill was evaluated using a modified logarithmic score. We averaged submitted forecasts into a mean ensemble model and compared them against predictions based on historical trends. Forecast skill was highest for seasonal peak intensity and short-term forecasts, while forecast skill for timing of season onset and peak week was generally low. Higher forecast skill was associated with team participation in previous influenza forecasting challenges and utilization of ensemble forecasting techniques. The mean ensemble consistently performed well and outperformed historical trend predictions. CDC and contributing teams will continue to advance influenza forecasting and work to improve the accuracy and reliability of forecasts to facilitate increased incorporation into public health response efforts.

Summary results of the 2014-2015 DARPA Chikungunya challenge

Background: Emerging pathogens such as Zika, chikungunya, Ebola, and dengue viruses are serious threats to national and global health security. Accurate forecasts of emerging epidemics and their severity are critical to minimizing subsequent mortality, morbidity, and economic loss. The recent introduction of chikungunya and Zika virus to the Americas underscores the need for better methods for disease surveillance and forecasting.

Methods: To explore the suitability of current approaches to forecasting emerging diseases, the Defense Advanced Research Projects Agency (DARPA) launched the 2014–2015 DARPA Chikungunya Challenge to forecast the number of cases and spread of chikungunya disease in the Americas. Challenge participants (n=38 during final evaluation) provided predictions of chikungunya epidemics across the Americas for a six-month period, from September 1, 2014 to February 16, 2015, to be evaluated by comparison with incidence data reported to the Pan American Health Organization (PAHO). This manuscript presents an overview of the challenge and a summary of the approaches used by the winners.

Results: Participant submissions were evaluated by a team of non-competing government subject matter experts based on numerical accuracy and methodology. Although this manuscript does not include in-depth analyses of the results, cursory analyses suggest that simpler models appear to outperform more complex approaches that included, for example, demographic information and transportation dynamics, due to the reporting biases, which can be implicitly captured in statistical models. Mosquito-dynamics, population specific information, and dengue-specific information correlated best with prediction accuracy.

Conclusion: We conclude that with careful consideration and understanding of the relative advantages and disadvantages of particular methods, implementation of an effective prediction system is feasible. However, there is a need to improve the quality of the data in order to more accurately predict the course of epidemics.

Aedes aegypti (Diptera: Culicidae) Abundance Model Improved With Relative Humidity and Precipitation-Driven Egg Hatching

We propose an improved Aedes aegypti (L.) abundance model that takes into account the effect of relative humidity (RH) on adult survival, as well as rainfall-triggered egg hatching. The model uses temperature-dependent development rates described in the literature as well as documented estimates for mosquito survival in environments with high RH, and for egg desiccation. We show that combining the two additional components leads to better agreement with surveillance trap data and with dengue incidence reports in various municipalities of Puerto Rico than incorporating either alone or neither. Capitalizing on the positive association between disease incidence and vector abundance, this improved model is therefore useful to estimate incidence of Ae. aegypti-borne diseases in locations where the vector is abundant year-round.