The challenges of modeling and forecasting the spread of COVID-19

Stratified epidemic model using a latent marked Hawkes process

We extend the unstructured homogeneously mixing epidemic model introduced by Lamprinakou et al. (2023) to a finite population stratified by age bands. We model the actual unobserved infections using a latent marked Hawkes process and the reported aggregated infections as random quantities driven by the underlying Hawkes process. We apply a Kernel Density Particle Filter (KDPF) to infer the marked counting process, the instantaneous reproduction number for each age group and forecast the epidemic's trajectory in the near future. Taking into account the individual inhomogeneity in age does not increase significantly the computational cost of the proposed inference algorithm compared to the cost of the proposed algorithm for the homogeneously unstructured epidemic model. We demonstrate that considering the individual heterogeneity in age, we can derive the instantaneous reproduction numbers per age group that provide a real-time measurement of interventions and behavioural changes of the associated groups. We illustrate the performance of the proposed inference algorithm on synthetic data sets and COVID-19-reported cases in various local authorities in the UK, and benchmark our model to the unstructured homogeneously mixing epidemic model. Our paper is a "demonstration" of a methodology that might be applied to factors other than age for stratification.

Trends in SARS-CoV-2 Cycle Threshold Values in Bosnia and Herzegovina-A Retrospective Study

The emergence of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), which led to the COVID-19 pandemic, has significantly impacted global public health. The proper diagnosis of SARS-CoV-2 infection is essential for the effective control and management of the disease. This study investigated the SARS-CoV-2 infection using RT-qPCR tests from laboratories in Bosnia and Herzegovina. We performed a retrospective study of demographic data and Ct values from 170,828 RT-qPCR tests from April 2020 to April 2023, representing 9.3% of total national testing. Samples were collected from 83,413 individuals across different age groups. Of all tests, 33.4% were positive for SARS-CoV-2, with Ct values and positivity rates varying across demographics and epidemic waves. The distribution was skewed towards older age groups, although lower positivity rates were observed in younger age groups. Ct values, indicative of viral load, ranged from 12.5 to 38. Lower Ct values correlated with higher positive case numbers, while higher Ct values signaled outbreak resolution. Additionally, Ct values decreased during epidemic waves but increased with the dominance of certain variants. Ct value-distribution has changed over time, particularly after the introduction of SARS-CoV-2 variants of interest/concern. Established Ct value trends might, therefore, be used as an early indicator and additional tool for informed decisions by public health authorities in SARS-CoV-2 and future prospective pandemics. Moreover, they should not be overlooked in future epidemiological events.

Modeling correlated uncertainties in stochastic compartmental models

We consider compartmental models of communicable disease with uncertain contact rates. Stochastic fluctuations are often added to the contact rate to account for uncertainties. White noise, which is the typical choice for the fluctuations, leads to significant underestimation of the disease severity. Here, starting from reasonable assumptions on the social behavior of individuals, we model the contacts as a Markov process which takes into account the temporal correlations present in human social activities. Consequently, we show that the mean-reverting Ornstein-Uhlenbeck (OU) process is the correct model for the stochastic contact rate. We demonstrate the implication of our model on two examples: a Susceptibles-Infected-Susceptibles (SIS) model and a Susceptibles-Exposed-Infected-Removed (SEIR) model of the COVID-19 pandemic and compare the results to the available US data from the Johns Hopkins University database. In particular, we observe that both compartmental models with white noise uncertainties undergo transitions that lead to the systematic underestimation of the spread of the disease. In contrast, modeling the contact rate with the OU process significantly hinders such unrealistic noise-induced transitions. For the SIS model, we derive its stationary probability density analytically, for both white and correlated noise. This allows us to give a complete description of the model's asymptotic behavior as a function of its bifurcation parameters, i.e., the basic reproduction number, noise intensity, and correlation time. For the SEIR model, where the probability density is not available in closed form, we study the transitions using Monte Carlo simulations. Our modeling approach can be used to quantify uncertain parameters in a broad range of biological systems.

Month-to-month all-cause mortality forecasting: a method allowing for changes in seasonal patterns

Forecasting of seasonal mortality patterns can provide useful information for planning health-care demand and capacity. Timely mortality forecasts are needed during severe winter spikes and/or pandemic waves to guide policy-making and public health decisions. In this article, we propose a flexible method for forecasting all-cause mortality in real time considering short-term changes in seasonal patterns within an epidemiologic year. All-cause mortality data have the advantage of being available with less delay than cause-specific mortality data. In this study, we use all-cause monthly death counts obtained from the national statistical offices of Denmark, France, Spain, and Sweden from epidemic seasons 2012-2013 through 2021-2022 to demonstrate the performance of the proposed approach. The method forecasts deaths 1 month ahead, based on their expected ratio to the next month. Prediction intervals are obtained via bootstrapping. The forecasts accurately predict the winter mortality peaks before the COVID-19 pandemic. Although the method predicts mortality less accurately during the first wave of the COVID-19 pandemic, it captures the aspects of later waves better than other traditional methods. The method is attractive for health researchers and governmental offices for aiding public health responses because it uses minimal input data, makes simple and intuitive assumptions, and provides accurate forecasts both during seasonal influenza epidemics and during novel virus pandemics.

Missing data in amortized simulation-based neural posterior estimation

Amortized simulation-based neural posterior estimation provides a novel machine learning based approach for solving parameter estimation problems. It has been shown to be computationally efficient and able to handle complex models and data sets. Yet, the available approach cannot handle the in experimental studies ubiquitous case of missing data, and might provide incorrect posterior estimates. In this work, we discuss various ways of encoding missing data and integrate them into the training and inference process. We implement the approaches in the BayesFlow methodology, an amortized estimation framework based on invertible neural networks, and evaluate their performance on multiple test problems. We find that an approach in which the data vector is augmented with binary indicators of presence or absence of values performs the most robustly. Indeed, it improved the performance also for the simpler problem of data sets with variable length. Accordingly, we demonstrate that amortized simulation-based inference approaches are applicable even with missing data, and we provide a guideline for their handling, which is relevant for a broad spectrum of applications.

Estimating vaccine efficacy during open-label follow-up of COVID-19 vaccine trials based on population-level surveillance data

While rapid development and roll out of COVID-19 vaccines is necessary in a pandemic, the process limits the ability of clinical trials to assess longer-term vaccine efficacy. We leveraged COVID-19 surveillance data in the U.S. to evaluate vaccine efficacy in U.S. Government-funded COVID-19 vaccine efficacy trials with a three-step estimation process. First, we used a compartmental epidemiological model informed by county-level surveillance data, a "population model", to estimate SARS-CoV-2 incidence among the unvaccinated. Second, a "cohort model" was used to adjust the population SARS-CoV-2 incidence to the vaccine trial cohort, taking into account individual participant characteristics and the difference between SARS-CoV-2 infection and COVID-19 disease. Third, we fit a regression model estimating the offset between the cohort-model-based COVID-19 incidence in the unvaccinated with the placebo-group COVID-19 incidence in the trial during blinded follow-up. Counterfactual placebo COVID-19 incidence was estimated during open-label follow-up by adjusting the cohort-model-based incidence rate by the estimated offset. Vaccine efficacy during open-label follow-up was estimated by contrasting the vaccine group COVID-19 incidence with the counterfactual placebo COVID-19 incidence. We documented good performance of the methodology in a simulation study. We also applied the methodology to estimate vaccine efficacy for the two-dose AZD1222 COVID-19 vaccine using data from the phase 3 U.S. trial (ClinicalTrials.gov # NCT04516746). We estimated AZD1222 vaccine efficacy of 59.1% (95% uncertainty interval (UI): 40.4%-74.3%) in April, 2021 (mean 106 days post-second dose), which reduced to 35.7% (95% UI: 15.0%-51.7%) in July, 2021 (mean 198 days post-second-dose). We developed and evaluated a methodology for estimating longer-term vaccine efficacy. This methodology could be applied to estimating counterfactual placebo incidence for future placebo-controlled vaccine efficacy trials of emerging pathogens with early termination of blinded follow-up, to active-controlled or uncontrolled COVID-19 vaccine efficacy trials, and to other clinical endpoints influenced by vaccination.

Projecting the future impact of emerging SARS-CoV-2 variants under uncertainty: Modeling the initial Omicron outbreak

Over the past several years, the emergence of novel SARS-CoV-2 variants has led to multiple waves of increased COVID-19 incidence. When the Omicron variant emerged, there was considerable concern about its potential impact in the winter of 2021-2022 due to its increased fitness. However, there was also considerable uncertainty regarding its likely impact due to questions about its relative transmissibility, severity, and degree of immune escape. We sought to evaluate the ability of an agent-based model to forecast incidence in the context of this emerging pathogen variant. To project COVID-19 cases and deaths in Indiana, we calibrated our model to COVID-19 hospitalizations, deaths, and test-positivity rates through November 2021, and then projected COVID-19 incidence through April 2022 under four different scenarios that covered the plausible ranges of Omicron's severity, transmissibility, and degree of immune escape. Our initial projections from December 2021 through March 2022 indicated that under a pessimistic scenario with high disease severity, the peak in weekly COVID-19 deaths in Indiana would be larger than the previous peak in December 2020. However, retrospective analyses indicate that Omicron's severity was closer to the optimistic scenario, and even though cases and hospitalizations reached a new peak, fewer deaths occurred than during the previous peak. According to our results, Omicron's rapid spread was consistent with a combination of higher transmissibility and immune escape relative to earlier variants. Our updated projections starting in January 2022 accurately predicted that cases would peak in mid-January and decline rapidly over the next several months. The performance of our projections shows that following the emergence of a new pathogen variant, models can help quantify the potential range of outbreak magnitudes and trajectories. Agent-based models are particularly useful in these scenarios because they can efficiently track individual vaccination and infection histories with multiple variants with varying degrees of cross-protection.

Parameter estimation in behavioral epidemic models with endogenous societal risk-response

Behavioral epidemic models incorporating endogenous societal risk-response, where changes in risk perceptions prompt adjustments in contact rates, are crucial for predicting pandemic trajectories. Accurate parameter estimation in these models is vital for validation and precise projections. However, few studies have examined the problem of identifiability in models where disease and behavior parameters must be jointly estimated. To address this gap, we conduct simulation experiments to assess the effect on parameter estimation accuracy of a) delayed risk response, b) neglecting behavioral response in model structure, and c) integrating disease and public behavior data. Our findings reveal systematic biases in estimating behavior parameters even with comprehensive and accurate disease data and a well-structured simulation model when data are limited to the first wave. This is due to the significant delay between evolving risks and societal reactions, corresponding to the duration of a pandemic wave. Moreover, we demonstrate that conventional SEIR models, which disregard behavioral changes, may fit well in the early stages of a pandemic but exhibit significant errors after the initial peak. Furthermore, early on, relatively small data samples of public behavior, such as mobility, can significantly improve estimation accuracy. However, the marginal benefits decline as the pandemic progresses. These results highlight the challenges associated with the joint estimation of disease and behavior parameters in a behavioral epidemic model.

The impacts of spatial-temporal heterogeneity of human-to-human contacts on the extinction probability of infectious disease from branching process model

In this study, we focus on the impacts of spatial-temporal heterogeneity of human-to-human contacts on the spread of infectious diseases and develop a multi-type branching process model by introducing random human-to-human contact mode into a structured population. We provide the general formulas of the generation size, extinction probability, and basic reproduction number of the proposed branching process model. The result shows that the natural temporal heterogeneity (i.e. random contacts over time) can lead to a higher extinction probability while remains the same basic reproduction number and generation size. This is also numerically verified by choosing the real contact distributions from different circumstances of four countries. In addition, we observe a non-monotonic pattern of the differences, against the transmission probability and the mean contact rate, between the extinction probabilities under the constant and random contact patterns. Given the spatial heterogeneity, we show that it can contribute to the increase of basic reproduction number, but also increase the extinction probability of the infectious disease. This study adds novel insights to the course of the impact of heterogeneity on the transmission dynamics and also provides additional evidence for the limited role of reproduction numbers.

Beyond linear regression: Modeling COVID-19 clinical cases with wastewater surveillance of SARS-CoV-2 for the city of Athens and Ohio University campus

Wastewater-based surveillance has emerged as a detection tool for population-wide infectious diseases, including coronavirus disease 2019 (COVID-19), caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Infected individuals shed the virus, which can be detected in wastewater using molecular techniques such as reverse transcription-digital polymerase chain reaction (RT-dPCR). This study examined the association between the number of clinical cases and the concentration of SARS-CoV-2 in wastewater beyond linear regression and for various normalizations of viral loads. Viral loads were measured in a total of 446 wastewater samples during the period from August 2021 to April 2022. These samples were collected from nine different locations, with 220 samples taken from four specific sites within the city of Athens and 226 samples from five sites within Ohio University. The correlation between COVID-19 cases and wastewater viral concentrations, which was estimated using the Pearson correlation coefficient, was statistically significant and ranged from 0.6 to 0.9. In addition, time-lagged cross correlation was applied to identify the lag time between clinical and wastewater data, estimated 4 to 7 days. While we also explored the effect on the correlation coefficients of various normalizations of viral loads accounting for procedural loss or amount of fecal material and of estimated lag times, these alternative specifications did not change our substantive conclusions. Additionally, several linear and non-linear regression models were applied to predict the COVID-19 cases given wastewater data as input. The non-linear approach was found to yield the highest R-squared and Pearson correlation and lowest Mean Absolute Error values between the predicted and actual number of COVID-19 cases for both aggregated OHIO Campus and city data. Our results provide support for previous studies on correlation and time lag and new evidence that non-linear models, approximated with artificial neural networks, should be implemented for WBS of contagious diseases.

Stochastic transmission in epidemiological models

Recent empirical evidence suggests that the transmission coefficient in susceptible-exposed-infected-removed-like (SEIR-like) models evolves with time, presenting random patterns, and some stylized facts, such as mean-reversion and jumps. To address such observations we propose the use of jump-diffusion stochastic processes to parameterize the transmission coefficient in an SEIR-like model that accounts for death and time-dependent parameters. We provide a detailed theoretical analysis of the proposed model proving the existence and uniqueness of solutions as well as studying its asymptotic behavior. We also compare the proposed model with some variations possibly including jumps. The forecast performance of the considered models, using reported COVID-19 infections from New York City, is then tested in different scenarios. Despite the simplicity of the epidemiological model, by considering stochastic transmission, the forecasted scenarios were fairly accurate.

Synchronization of non-smooth chaotic systems via an improved reservoir computing

The reservoir computing (RC) is increasingly used to learn the synchronization behavior of chaotic systems as well as the dynamical behavior of complex systems, but it is scarcely applied in studying synchronization of non-smooth chaotic systems likely due to its complexity leading to the unimpressive effect. Here proposes a simulated annealing-based differential evolution (SADE) algorithm for the optimal parameter selection in the reservoir, and constructs an improved RC model for synchronization, which can work well not only for non-smooth chaotic systems but for smooth ones. Extensive simulations show that the trained RC model with optimal parameters has far longer prediction time than those with empirical and random parameters. More importantly, the well-trained RC system can be well synchronized to its original chaotic system as well as its replicate RC system via one shared signal, whereas the traditional RC system with empirical or random parameters fails for some chaotic systems, particularly for some non-smooth chaotic systems.

Vaccination compartmental epidemiological models for the delta and omicron SARS-CoV-2 variants

We explore the inclusion of vaccination in compartmental epidemiological models concerning the delta and omicron variants of the SARS-CoV-2 virus that caused the COVID-19 pandemic. We expand on our earlier compartmental-model work by incorporating vaccinated populations. We present two classes of models that differ depending on the immunological properties of the variant. The first one is for the delta variant, where we do not follow the dynamics of the vaccinated individuals since infections of vaccinated individuals were rare. The second one for the far more contagious omicron variant incorporates the evolution of the infections within the vaccinated cohort. We explore comparisons with available data involving two possible classes of counts, fatalities and hospitalizations. We present our results for two regions, Andalusia and Switzerland (including the Principality of Liechtenstein), where the necessary data are available. In the majority of the considered cases, the models are found to yield good agreement with the data and have a reasonable predictive capability beyond their training window, rendering them potentially useful tools for the interpretation of the COVID-19 and further pandemic waves, and for the design of intervention strategies during these waves.

Predicting COVID-19 pandemic waves including vaccination data with deep learning

Introduction

During the recent COVID-19 pandemics, many models were developed to predict the number of new infections. After almost a year, models had also the challenge to include information about the waning effect of vaccines and by infection, and also how this effect start to disappear.

Methods

We present a deep learning-based approach to predict the number of daily COVID-19 cases in 30 countries, considering the non-pharmaceutical interventions (NPIs) applied in those countries and including vaccination data of the most used vaccines.

Results

We empirically validate the proposed approach for 4 months between January and April 2021, once vaccination was available and applied to the population and the COVID-19 variants were closer to the one considered for developing the vaccines. With the predictions of new cases, we can prescribe NPIs plans that present the best trade-off between the expected number of COVID-19 cases and the social and economic cost of applying such interventions.

Discussion

Whereas, mathematical models which include the effect of vaccines in the spread of the SARS-COV-2 pandemic are available, to the best of our knowledge we are the first to propose a data driven method based on recurrent neural networks that considers the waning effect of the immunization acquired either by vaccine administration or by recovering from the illness. This work contributes with an accurate, scalable, data-driven approach to modeling the pandemic curves of cases when vaccination data is available.

A data-driven semi-parametric model of SARS-CoV-2 transmission in the United States

To support decision-making and policy for managing epidemics of emerging pathogens, we present a model for inference and scenario analysis of SARS-CoV-2 transmission in the USA. The stochastic SEIR-type model includes compartments for latent, asymptomatic, detected and undetected symptomatic individuals, and hospitalized cases, and features realistic interval distributions for presymptomatic and symptomatic periods, time varying rates of case detection, diagnosis, and mortality. The model accounts for the effects on transmission of human mobility using anonymized mobility data collected from cellular devices, and of difficult to quantify environmental and behavioral factors using a latent process. The baseline transmission rate is the product of a human mobility metric obtained from data and this fitted latent process. We fit the model to incident case and death reports for each state in the USA and Washington D.C., using likelihood Maximization by Iterated particle Filtering (MIF). Observations (daily case and death reports) are modeled as arising from a negative binomial reporting process. We estimate time-varying transmission rate, parameters of a sigmoidal time-varying fraction of hospitalized cases that result in death, extra-demographic process noise, two dispersion parameters of the observation process, and the initial sizes of the latent, asymptomatic, and symptomatic classes. In a retrospective analysis covering March-December 2020, we show how mobility and transmission strength became decoupled across two distinct phases of the pandemic. The decoupling demonstrates the need for flexible, semi-parametric approaches for modeling infectious disease dynamics in real-time.

Assessment of a SARS-CoV-2 population-wide rapid antigen testing in Italy: a modeling and economic analysis study

BACKGROUND

This study aimed to compare the cost-effectiveness of coronavirus disease 2019 (COVID-19) mass testing, carried out in November 2020 in the Italian Bolzano/Südtirol province, to scenarios without mass testing in terms of hospitalizations averted and quality-adjusted life-year (QALYs) saved.

METHODS

We applied branching processes to estimate the effective reproduction number (Rt) and model scenarios with and without mass testing, assuming Rt = 0.9 and Rt = 0.95. We applied a bottom-up approach to estimate the costs of mass testing, with a mixture of bottom-up and top-down methodologies to estimate hospitalizations averted and incremental costs in case of non-intervention. Lastly, we estimated the incremental cost-effectiveness ratio (ICER), denoted by screening and related social costs, and hospitalization costs averted per outcome derived, hospitalizations averted and QALYs saved.

RESULTS

The ICERs per QALY were €24 249 under Rt = 0.9 and €4604 under Rt = 0.95, considering the official and estimated data on disease spread. The cost-effectiveness acceptability curves show that for the Rt = 0.9 scenario, at the maximum threshold willingness to pay the value of €40 000, mass testing has an 80% probability of being cost-effective compared to no mass testing. Under the worst scenario (Rt = 0.95), at the willingness to pay threshold, mass testing has an almost 100% probability of being cost-effective.

CONCLUSIONS

We provide evidence on the cost-effectiveness and potential impact of mass COVID-19 testing on a local healthcare system and community. Although the intervention is shown to be cost-effective, we believe the initiative should be carried out when there is initial rapid local disease transmission with a high Rt, as shown in our model.

Health behavior in Russia during the COVID-19 pandemic

In this article, we report results from a nationwide survey on pandemic-related health behavior in Russia. A total of 2,771 respondents aged 18 to 82 were interviewed between January 21 and March 3, 2021. The survey included questions on perceived vulnerability to coronavirus, prevention-related health behavior, readiness for vaccination, and general awareness about COVID-19. Descriptive data showed that 21.2% of respondents reported high vulnerability to the coronavirus, and 25% expressed fear. Moreover, 38.7% of the surveyed individuals reported low trust in vaccination efficacy, and 57.5% were unwilling to take a vaccine, which was much higher than the official data. Based on the evidence obtained, four types of health behavior during the pandemic were constructed. Rational (29.3%) and denying (28.6%) behaviors prevailed in men, while women were found to more likely behave with a vaccine-hesitant demeanor (35.7%). Educational background affected the proportion of respondents with the denying type of health behavior, who were also of younger age. The rational behavioral type was found to be more common among respondents aged above 50 years and prevailed as well among individuals with university degrees. The middle-aged population of Russia was highly compliant with prevention-related health practices; however, vaccine hesitancy was also high among them. Furthermore, health behaviors varied significantly across the Federal Districts of Russia. We are convinced that our results contribute to existing public health practices and may help improve communication campaigns to cause positive health behaviors.

Development and Validation of the US Diabetes, Obesity, Cardiovascular Disease Microsimulation (DOC-M) Model: Health Disparity and Economic Impact Model

BACKGROUND

Few simulation models have incorporated the interplay of diabetes, obesity, and cardiovascular disease (CVD); their upstream lifestyle and biological risk factors; and their downstream effects on health disparities and economic consequences.

METHODS

We developed and validated a US Diabetes, Obesity, Cardiovascular Disease Microsimulation (DOC-M) model that incorporates demographic, clinical, and lifestyle risk factors to jointly predict overall and racial-ethnic groups-specific obesity, diabetes, CVD, and cause-specific mortality for the US adult population aged 40 to 79 y at baseline. An individualized health care cost prediction model was further developed and integrated. This model incorporates nationally representative data on baseline demographics, lifestyle, health, and cause-specific mortality; dynamic changes in modifiable risk factors over time; and parameter uncertainty using probabilistic distributions. Validation analyses included assessment of 1) population-level risk calibration and 2) individual-level risk discrimination. To illustrate the application of the DOC-M model, we evaluated the long-term cost-effectiveness of a national produce prescription program.

RESULTS

Comparing the 15-y model-predicted population risk of primary outcomes among the 2001-2002 National Health and Nutrition Examination Survey (NHANES) cohort with the observed prevalence from age-matched cross-sectional 2003-2016 NHANES cohorts, calibration performance was strong based on observed-to-expected ratio and calibration plot analysis. In most cases, Brier scores fell below 0.0004, indicating a low overall prediction error. Using the Multi-Ethnic Study of Atherosclerosis cohorts, the c-statistics for assessing individual-level risk discrimination were 0.85 to 0.88 for diabetes, 0.93 to 0.95 for obesity, 0.74 to 0.76 for CVD history, and 0.78 to 0.81 for all-cause mortality, both overall and in three racial-ethnic groups. Open-source code for the model was posted at https://github.com/food-price/DOC-M-Model-Development-and-Validation.

CONCLUSIONS

The validated DOC-M model can be used to examine health, equity, and the economic impact of health policies and interventions on behavioral and clinical risk factors for obesity, diabetes, and CVD.

HIGHLIGHTS

We developed a novel microsimula'tion model for obesity, diabetes, and CVD, which intersect together and - critically for prevention and treatment interventions - share common lifestyle, biologic, and demographic risk factors.Validation analyses, including assessment of (1) population-level risk calibration and (2) individual-level risk discrimination, showed strong performance across the overall population and three major racial-ethnic groups for 6 outcomes (obesity, diabetes, CVD, and all-cause mortality, CVD- and DM-cause mortality)This paper provides a thorough explanation and documentation of the development and validation process of a novel microsimulation model, along with the open-source code (https://github.com/food-price/ DOCM_validation) for public use, to serve as a guide for future simulation model assessments, validation, and implementation.

Birth and early parenting during the COVID-19 pandemic: A cross-sectional study in the Austrian and German population

BACKGROUND

During the COVID-19 pandemic, new mothers and their babies represent a particularly vulnerable group. This study investigates the effects of the pandemic on the pregnancy and childbirth experience, as well as on postnatal stress and depression levels.

METHODS

An online survey was completed by 1964 Austrian and German mothers who gave birth during the COVID-19 pandemic. The survey included the Pregnancy Distress Questionnaire (PDQ), the Childbirth Experience Questionnaire (CEQ), the Edinburgh Postnatal Depression Score (EPDS), the Perceived Stress Score (PSS), and additional pregnancy- and pandemic-related questions. We conducted multilinear regression models in order to investigate which factors predict childbirth experience, stress and depression scores.

FINDINGS

There was a high prevalence of depression symptoms (42%), though the mean EPDS score was 8·71 (SD = 5·70), below the cut-off for depression of 10. The prevalence of high stress scores was 9%, and the mean PSS score was 17·7 (SD = 6·64), which indicates moderate perceived stress. The pandemic reduced the time spent with grandparents, as well as the help received by the mother from relatives and friends. Not receiving help was associated with higher stress and depression scores. In the multilinear regression models, the most important predictor for a negative childbirth experience was a high-risk pregnancy, while the strongest predictors for high stress and depression levels were low social support and negatively perceived pandemic repercussions on financial, social or health aspects of family life.

INTERPRETATION

The results suggest that the pandemic had an impact on maternal mental health. While the perceived consequences due to the pandemic negatively affected the postnatal depression and stress levels, perceived social support acted as a protective factor.

Disentangling the role of virus infectiousness and awareness-based human behavior during the early phase of the COVID-19 pandemic in the European Union

In this work, we manage to disentangle the role of virus infectiousness and awareness-based human behavior in the COVID-19 pandemic. Using Bayesian inference, we quantify the uncertainty of a state-space model whose propagator is based on an unusual SEIR-type model since it incorporates the effective population fraction as a parameter. Within the Markov Chain Monte Carlo (MCMC) algorithm, Unscented Kalman Filter (UKF) may be used to evaluate the likelihood approximately. UKF is a suitable strategy in many cases, but it is not well-suited to deal with non-negativity restrictions on the state variables. To overcome this difficulty, we modify the UKF, conveniently truncating Gaussian distributions, which allows us to deal with such restrictions. We use official infection notification records to analyze the first 22 weeks of infection spread in each of the 27 countries of the European Union (EU). It is known that such records are the primary source of information to assess the early evolution of the pandemic and, at the same time, usually suffer underreporting and backlogs. Our model explicitly accounts for uncertainty in the dynamic model parameters, the dynamic model adequacy, and the infection observation process. We argue that this modeling paradigm allows us to disentangle the role of the contact rate, the effective population fraction, and the infection observation probability across time and space with an imperfect first principles model. Our findings agree with phylogenetic evidence showing little variability in the contact rate, or virus infectiousness, across EU countries during the early phase of the pandemic, highlighting the advantage of incorporating the effective population fraction into pandemic modeling for heterogeneity in both human behavior and reporting. Finally, to evaluate the consistency of our data assimilation method, we performed a forecast that adequately fits the actual data.

Statement of significance

Data-driven and model-based epidemiological studies aimed at learning the number of people infected early during a pandemic should explicitly consider the behavior-induced effective population effect. Indeed, the non-isolated, or effective, fraction of the population during the early phase of the pandemic is time-varying, and first-principles modeling with quantified uncertainty is imperative for an adequate analysis across time and space. We argue that, although good inference results may be obtained using the classical SEIR type model, the model posed in this work has allowed us to disentangle the role of virus infectiousness and awareness-based human behavior during the early phase of the COVID-19 pandemic in the European Union from official infection notification records.

REAL-TIME MECHANISTIC BAYESIAN FORECASTS OF COVID-19 MORTALITY

The COVID-19 pandemic emerged in late December 2019. In the first six months of the global outbreak, the U.S. reported more cases and deaths than any other country in the world. Effective modeling of the course of the pandemic can help assist with public health resource planning, intervention efforts, and vaccine clinical trials. However, building applied forecasting models presents unique challenges during a pandemic. First, case data available to models in real time represent a nonstationary fraction of the true case incidence due to changes in available diagnostic tests and test-seeking behavior. Second, interventions varied across time and geography leading to large changes in transmissibility over the course of the pandemic. We propose a mechanistic Bayesian model that builds upon the classic compartmental susceptible-exposed-infected-recovered (SEIR) model to operationalize COVID-19 forecasting in real time. This framework includes nonparametric modeling of varying transmission rates, nonparametric modeling of case and death discrepancies due to testing and reporting issues, and a joint observation likelihood on new case counts and new deaths; it is implemented in a probabilistic programming language to automate the use of Bayesian reasoning for quantifying uncertainty in probabilistic forecasts. The model has been used to submit forecasts to the U.S. Centers for Disease Control through the COVID-19 Forecast Hub under the name MechBayes. We examine the performance relative to a baseline model as well as alternate models submitted to the forecast hub. Additionally, we include an ablation test of our extensions to the classic SEIR model. We demonstrate a significant gain in both point and probabilistic forecast scoring measures using MechBayes, when compared to a baseline model, and show that MechBayes ranks as one of the top two models out of nine which regularly submitted to the COVID-19 Forecast Hub for the duration of the pandemic, trailing only the COVID-19 Forecast Hub ensemble model of which which MechBayes is a part.

Optimized numerical solutions of SIRDVW multiage model controlling SARS-CoV-2 vaccine roll out: An application to the Italian scenario

In the context of SARS-CoV-2 pandemic, mathematical modelling has played a fundamental role for making forecasts, simulating scenarios and evaluating the impact of preventive political, social and pharmaceutical measures. Optimal control theory represents a useful mathematical tool to plan the vaccination campaign aimed at eradicating the pandemic as fast as possible. The aim of this work is to explore the optimal prioritisation order for planning vaccination campaigns able to achieve specific goals, as the reduction of the amount of infected, deceased and hospitalized in a given time frame, among age classes. For this purpose, we introduce an age stratified SIR-like epidemic compartmental model settled in an abstract framework for modelling two-doses vaccination campaigns and conceived with the description of COVID19 disease. Compared to other recent works, our model incorporates all stages of the COVID-19 disease, including death or recovery, without accounting for additional specific compartments that would increase computational complexity and that are not relevant for our purposes. Moreover, we introduce an optimal control framework where the model is the state problem while the vaccine doses administered are the control variables. An extensive campaign of numerical tests, featured in the Italian scenario and calibrated on available data from Dipartimento di Protezione Civile Italiana, proves that the presented framework can be a valuable tool to support the planning of vaccination campaigns. Indeed, in each considered scenario, our optimization framework guarantees noticeable improvements in terms of reducing deceased, infected or hospitalized individuals with respect to the baseline vaccination policy.

Comparison of homemade mask designs based on calculated infection risk, using actual COVID-19 infection scenarios

During pandemics such as COVID-19, shortages of approved respirators necessitate the use of alternative masks, including homemade designs. The effectiveness of the masks is often quantified in terms of the ability to filter particles. However, to formulate public policy the efficacy of the mask in reducing the risk of infection for a given population is considerably more useful than its filtration efficiency (FE). The effect of the mask on the infection profile is complicated to estimate as it depends strongly upon the behavior of the affected population. A recently introduced tool known as the dynamic-spread model is well suited for performing population-specific risk assessment. The dynamic-spread model was used to simulate the performance of a variety of mask designs (all used for source control only) in different COVID-19 scenarios. The efficacy of different masks was found to be highly scenario dependent. Switching from a cotton T-shirt of 8% FE to a 3-layer cotton-gauze-cotton mask of 44% FE resulted in a decrease in number of new infections of about 30% in the New York State scenario and 60% in the Harris County, Texas scenario. The results are valuable to policy makers for quantifying the impact upon the infection rate for different intervention strategies, e.g., investing resources to provide the community with higher-filtration masks.

Estimation of self-exciting point processes from time-censored data

Self-exciting point processes, widely used to model arrival phenomena in nature and society, are often difficult to identify. The estimation becomes even more challenging when arrivals are recorded only as bin counts on a finite partition of the observation interval. In this paper, we propose the recursive identification with sample correction (RISC) algorithm for the estimation of process parameters from time-censored data. In every iteration, a synthetic sample path is generated and corrected to match the observed bin counts. Then the process parameters update and a unique iteration is performed to successively approximate the stochastic characteristics of the observed process. In terms of finite-sample approximation error, the proposed RISC framework performs favorably over extant methods, as well as compared to a naïve locally uniform sample redistribution. The results of an extensive numerical experiment indicate that the reconstruction of an intrabin history based on the conditional intensity of the process is crucial for attaining superior performance in terms of estimation error.

Deep reinforcement learning framework for controlling infectious disease outbreaks in the context of multi-jurisdictions

In the absence of pharmaceutical interventions, social distancing and lockdown have been key options for controlling new or reemerging respiratory infectious disease outbreaks. The timely implementation of these interventions is vital for effectively controlling and safeguarding the economy.Motivated by the COVID-19 pandemic, we evaluated whether, when, and to what level lockdowns are necessary to minimize epidemic and economic burdens of new disease outbreaks. We formulated the question as a sequential decision-making Markov Decision Process and solved it using deep Q-network algorithm. We evaluated the question under two objective functions: a 2-objective function to minimize economic burden and hospital capacity violations, suitable for diseases with severe health risks but with minimal death, and a 3-objective function that additionally minimizes the number of deaths, suitable for diseases that have high risk of mortality.A key feature of the model is that we evaluated the above questions in the context of two-geographical jurisdictions that interact through travel but make autonomous and independent decisions, evaluating under cross-jurisdictional cooperation and non-cooperation. In the 2-objective function under cross-jurisdictional cooperation, the optimal policy was to aim for shutdowns at 50 and 25% per day. Though this policy avoided hospital capacity violations, the shutdowns extended until a large proportion of the population reached herd immunity. Delays in initiating this optimal policy or non-cooperation from an outside jurisdiction required shutdowns at a higher level of 75% per day, thus adding to economic burdens. In the 3-objective function, the optimal policy under cross-jurisdictional cooperation was to aim for shutdowns of up to 75% per day to prevent deaths by reducing infected cases. This optimal policy continued for the entire duration of the simulation, suggesting that, until pharmaceutical interventions such as treatment or vaccines become available, contact reductions through physical distancing would be necessary to minimize deaths. Deviating from this policy increased the number of shutdowns and led to several deaths.In summary, we present a decision-analytic methodology for identifying optimal lockdown strategy under the context of interactions between jurisdictions that make autonomous and independent decisions. The numerical analysis outcomes are intuitive and, as expected, serve as proof of the feasibility of such a model. Our sensitivity analysis demonstrates that the optimal policy exhibits robustness to minor alterations in the transmission rate, yet shows sensitivity to more substantial deviations. This finding underscores the dynamic nature of epidemic parameters, thereby emphasizing the necessity for models trained across a diverse range of values to ensure effective policy-making.

Forecasting Pathogen Dynamics with Bayesian Model-Averaging: Application to Xylella fastidiosa

Forecasting invasive-pathogen dynamics is paramount to anticipate eradication and containment strategies. Such predictions can be obtained using a model grounded on partial differential equations (PDE; often exploited to model invasions) and fitted to surveillance data. This framework allows the construction of phenomenological but concise models relying on mechanistic hypotheses and real observations. However, it may lead to models with overly rigid behavior and possible data-model mismatches. Hence, to avoid drawing a forecast grounded on a single PDE-based model that would be prone to errors, we propose to apply Bayesian model averaging (BMA), which allows us to account for both parameter and model uncertainties. Thus, we propose a set of different competing PDE-based models for representing the pathogen dynamics, we use an adaptive multiple importance sampling algorithm (AMIS) to estimate parameters of each competing model from surveillance data in a mechanistic-statistical framework, we evaluate the posterior probabilities of models by comparing different approaches proposed in the literature, and we apply BMA to draw posterior distributions of parameters and a posterior forecast of the pathogen dynamics. This approach is applied to predict the extent of Xylella fastidiosa in South Corsica, France, a phytopathogenic bacterium detected in situ in Europe less than 10 years ago (Italy 2013, France 2015). Separating data into training and validation sets, we show that the BMA forecast outperforms competing forecast approaches.

Assessing needs-based supply of physicians: a criteria-led methodological review of international studies in high-resource settings

BACKGROUND

Many health systems embrace the normative principle that the supply of health services ought to be based on the need for healthcare. However, a theoretically grounded framework to operationalize needs-based supply of healthcare remains elusive. The aim of this paper is to critically assess current methodologies that quantify needs-based supply of physicians and identify potential gaps in approaches for physician planning. To this end, we propose a set of criteria for consideration when estimating needs-based supply.

METHODS

We conducted searches in three electronic bibliographic databases until March 2020 supplemented by targeted manual searches on national and international websites to identify studies in high-resource settings that quantify needs-based supply of physicians. Studies that exclusively focused on forecasting methods of physician supply, on inpatient care or on healthcare professionals other than physicians were excluded. Additionally, records that were not available in English or German were excluded to avoid translation errors. The results were synthesized using a framework of study characteristics in addition to the proposed criteria for estimating needs-based physician supply.

RESULTS

18 quantitative studies estimating population need for physicians were assessed against our criteria. No study met all criteria. Only six studies sought to examine the conceptual dependency between need, utilization and supply. Apart from extrapolations, simulation models were applied most frequently to estimate needs-based supply. 12 studies referred to the translation of need for services with respect to a physician's productivity, while the rest adapted existing population-provider-ratios. Prospective models for estimating future care needs were largely based on demographic predictions rather than estimated trends in morbidity and new forms of care delivery.

CONCLUSIONS

The methodological review shows distinct heterogeneity in the conceptual frameworks, validity of data basis and modeling approaches of current studies in high-resource settings on needs-based supply of physicians. To support future estimates of needs-based supply, this review provides a workable framework for policymakers in charge of health workforce capacity planning.

Seeing the forest and the trees: Holistic view of social distancing on the spread of COVID-19 in China

The human social and behavioral activities play significant roles in the spread of COVID-19. Social-distancing centered non-pharmaceutical interventions (NPIs) are the best strategies to curb the spread of COVID-19 prior to an effective pharmaceutical or vaccine solution. This study investigates various social-distancing measures' impact on the spread of COVID-19 using advanced global and novel local geospatial techniques. Social distancing measures are acquired through website analysis, document text analysis, and other big data extraction strategies. A spatial panel regression model and a newly proposed geographically weighted panel regression model are applied to investigate the global and local relationships between the spread of COVID-19 and the various social distancing measures. Results from the combined global and local analyses confirm the effectiveness of NPI strategies to curb the spread of COVID-19. While global level strategies allow a nation to implement social distancing measures immediately at the beginning to minimize the impact of the disease, local level strategies fine tune such measures based on different times and places to provide targeted implementation to balance conflicting demands during the pandemic. The local level analysis further suggests that implementing different NPI strategies in different locations might allow us to battle unknown global pandemic more efficiently.

Prediction From Minimal Experience: How People Predict the Duration of an Ongoing Epidemic

People are known for good predictions in domains they have rich experience with, such as everyday statistics and intuitive physics. But how well can they predict for problems they lack experience with, such as the duration of an ongoing epidemic caused by a new virus? Amid the first wave of COVID-19 in China, we conducted an online diary study, asking each of over 400 participants to predict the remaining duration of the epidemic, once per day for 14 days. Participants' predictions reflected a reasonable use of publicly available information but were meanwhile biased, subject to the influence of negative affect and future time perspectives. Computational modeling revealed that participants neither relied on prior distributions of epidemic durations as in inferring everyday statistics, nor on mechanistic simulations of epidemic dynamics as in computing intuitive physics. Instead, with minimal experience, participants' predictions were best explained by similarity-based generalization of the temporal pattern of epidemic statistics. In two control experiments, we further confirmed that such cognitive algorithm is not specific to the epidemic scenario and that minimal and rich experience do lead to different prediction behaviors for the same observations. We conclude that people generalize patterns in recent history to predict the future under minimal experience.

Assessing the accuracy of California county level COVID-19 hospitalization forecasts to inform public policy decision making

BACKGROUND

The COVID-19 pandemic has highlighted the role of infectious disease forecasting in informing public policy. However, significant barriers remain for effectively linking infectious disease forecasts to public health decision making, including a lack of model validation. Forecasting model performance and accuracy should be evaluated retrospectively to understand under which conditions models were reliable and could be improved in the future.

METHODS

Using archived forecasts from the California Department of Public Health's California COVID Assessment Tool ( https://calcat.covid19.ca.gov/cacovidmodels/ ), we compared how well different forecasting models predicted COVID-19 hospitalization census across California counties and regions during periods of Alpha, Delta, and Omicron variant predominance.

RESULTS

Based on mean absolute error estimates, forecasting models had variable performance across counties and through time. When accounting for model availability across counties and dates, some individual models performed consistently better than the ensemble model, but model rankings still differed across counties. Local transmission trends, variant prevalence, and county population size were informative predictors for determining which model performed best for a given county based on a random forest classification analysis. Overall, the ensemble model performed worse in less populous counties, in part because of fewer model contributors in these locations.

CONCLUSIONS

Ensemble model predictions could be improved by incorporating geographic heterogeneity in model coverage and performance. Consistency in model reporting and improved model validation can strengthen the role of infectious disease forecasting in real-time public health decision making.

An interpretable hybrid predictive model of COVID-19 cases using autoregressive model and LSTM

The Coronavirus Disease 2019 (COVID-19) has had a profound impact on global health and economy, making it crucial to build accurate and interpretable data-driven predictive models for COVID-19 cases to improve public policy making. The extremely large scale of the pandemic and the intrinsically changing transmission characteristics pose a great challenge for effectively predicting COVID-19 cases. To address this challenge, we propose a novel hybrid model in which the interpretability of the Autoregressive model (AR) and the predictive power of the long short-term memory neural networks (LSTM) join forces. The proposed hybrid model is formalized as a neural network with an architecture that connects two composing model blocks, of which the relative contribution is decided data-adaptively in the training procedure. We demonstrate the favorable performance of the hybrid model over its two single composing models as well as other popular predictive models through comprehensive numerical studies on two data sources under multiple evaluation metrics. Specifically, in county-level data of 8 California counties, our hybrid model achieves 4.173% MAPE, outperforming the composing AR (5.629%) and LSTM (4.934%) alone on average. In country-level datasets, our hybrid model outperforms the widely-used predictive models such as AR, LSTM, Support Vector Machines, Gradient Boosting, and Random Forest, in predicting the COVID-19 cases in Japan, Canada, Brazil, Argentina, Singapore, Italy, and the United Kingdom. In addition to the predictive performance, we illustrate the interpretability of our proposed hybrid model using the estimated AR component, which is a key feature that is not shared by most black-box predictive models for COVID-19 cases. Our study provides a new and promising direction for building effective and interpretable data-driven models for COVID-19 cases, which could have significant implications for public health policy making and control of the current COVID-19 and potential future pandemics.

Modeling the SARS-CoV-2 Omicron variant dynamics in the United States with booster dose vaccination and waning immunity

We carried out a theoretical and numerical analysis for an epidemic model to analyze the dynamics of the SARS-CoV-2 Omicron variant and the impact of vaccination campaigns in the United States. The model proposed here includes asymptomatic and hospitalized compartments, vaccination with booster doses, and the waning of natural and vaccine-acquired immunity. We also consider the influence of face mask usage and efficiency. We found that enhancing booster doses and using N95 face masks are associated with a reduction in the number of new infections, hospitalizations and deaths. We highly recommend the use of surgical face masks as well, if usage of N95 is not a possibility due to the price range. Our simulations show that there might be two upcoming Omicron waves (in mid-2022 and late 2022), caused by natural and acquired immunity waning with respect to time. The magnitude of these waves will be 53% and 25% lower than the peak in January 2022, respectively. Hence, we recommend continuing to use face masks to decrease the peak of the upcoming COVID-19 waves.

Assessing the transmissibility of epidemics involving epidemic zoning

BACKGROUND

Epidemic zoning is an important option in a series of measures for the prevention and control of infectious diseases. We aim to accurately assess the disease transmission process by considering the epidemic zoning, and we take two epidemics with distinct outbreak sizes as an example, i.e., the Xi'an epidemic in late 2021 and the Shanghai epidemic in early 2022.

METHODS

For the two epidemics, the total cases were clearly distinguished by their reporting zone and the Bernoulli counting process was used to describe whether one infected case in society would be reported in control zones or not. Assuming the imperfect or perfect isolation policy in control zones, the transmission processes are respectively simulated by the adjusted renewal equation with case importation, which can be derived on the basis of the Bellman-Harris branching theory. The likelihood function containing unknown parameters is then constructed by assuming the daily number of new cases reported in control zones follows a Poisson distribution. All the unknown parameters were obtained by the maximum likelihood estimation.

RESULTS

For both epidemics, the internal infections characterized by subcritical transmission within the control zones were verified, and the median control reproduction numbers were estimated as 0.403 (95% confidence interval (CI): 0.352, 0.459) in Xi'an epidemic and 0.727 (95% CI: 0.724, 0.730) in Shanghai epidemic, respectively. In addition, although the detection rate of social cases quickly increased to 100% during the decline period of daily new cases until the end of the epidemic, the detection rate in Xi'an was significantly higher than that in Shanghai in the previous period.

CONCLUSIONS

The comparative analysis of the two epidemics with different consequences highlights the role of the higher detection rate of social cases since the beginning of the epidemic and the reduced transmission risk in control zones throughout the outbreak. Strengthening the detection of social infection and strictly implementing the isolation policy are of great significance to avoid a larger-scale epidemic.

Trends in SARS-CoV-2 cycle threshold values in the Czech Republic from April 2020 to April 2022

The inability to predict the evolution of the COVID-19 epidemic hampered abilities to respond to the crisis effectively. The cycle threshold (Ct) from the standard SARS-CoV-2 quantitative reverse transcription-PCR (RT-qPCR) clinical assay is inversely proportional to the amount of SARS-CoV-2 RNA in the sample. We were interested to see if population Ct values could predict future increases in COVID-19 cases as well as subgroups that would be more likely to be affected. This information would have been extremely helpful early in the COVID-19 epidemic. We therefore conducted a retrospective analysis of demographic data and Ct values from 2,076,887 nasopharyngeal swab RT-qPCR tests that were performed at a single diagnostic laboratory in the Czech Republic from April 2020 to April 2022 and from 221,671 tests that were performed as a part of a mandatory school surveillance testing program from March 2021 to March 2022. We found that Ct values could be helpful predictive tools in the real-time management of viral epidemics. First, early measurement of Ct values would have indicated the low viral load in children, equivalent viral load in males and females, and higher viral load in older individuals. Second, rising or falling median Ct values and differences in Ct distribution indicated changes in the transmission in the population. Third, monitoring Ct values and positivity rates would have provided early evidence as to whether prevention measures are effective. Health system authorities should thus consider collecting weekly median Ct values of positively tested samples from major diagnostic laboratories for regional epidemic surveillance.

Complexity of Government response to COVID-19 pandemic: a perspective of coupled dynamics on information heterogeneity and epidemic outbreak

This study aims at modeling the universal failure in preventing the outbreak of COVID-19 via real-world data from the perspective of complexity and network science. Through formalizing information heterogeneity and government intervention in the coupled dynamics of epidemic and infodemic spreading, first, we find that information heterogeneity and its induced variation in human responses significantly increase the complexity of the government intervention decision. The complexity results in a dilemma between the socially optimal intervention that is risky for the government and the privately optimal intervention that is safer for the government but harmful to the social welfare. Second, via counterfactual analysis against the COVID-19 crisis in Wuhan, 2020, we find that the intervention dilemma becomes even worse if the initial decision time and the decision horizon vary. In the short horizon, both socially and privately optimal interventions agree with each other and require blocking the spread of all COVID-19-related information, leading to a negligible infection ratio 30 days after the initial reporting time. However, if the time horizon is prolonged to 180 days, only the privately optimal intervention requires information blocking, which would induce a catastrophically higher infection ratio than that in the counterfactual world where the socially optimal intervention encourages early-stage information spread. These findings contribute to the literature by revealing the complexity incurred by the coupled infodemic-epidemic dynamics and information heterogeneity to the governmental intervention decision, which also sheds insight into the design of an effective early warning system against the epidemic crisis in the future.

Using a latent Hawkes process for epidemiological modelling

Understanding the spread of COVID-19 has been the subject of numerous studies, highlighting the significance of reliable epidemic models. Here, we introduce a novel epidemic model using a latent Hawkes process with temporal covariates for modelling the infections. Unlike other models, we model the reported cases via a probability distribution driven by the underlying Hawkes process. Modelling the infections via a Hawkes process allows us to estimate by whom an infected individual was infected. We propose a Kernel Density Particle Filter (KDPF) for inference of both latent cases and reproduction number and for predicting the new cases in the near future. The computational effort is proportional to the number of infections making it possible to use particle filter type algorithms, such as the KDPF. We demonstrate the performance of the proposed algorithm on synthetic data sets and COVID-19 reported cases in various local authorities in the UK, and benchmark our model to alternative approaches.

TransCode: Uncovering COVID-19 transmission patterns via deep learning

BACKGROUND

The heterogeneity of COVID-19 spread dynamics is determined by complex spatiotemporal transmission patterns at a fine scale, especially in densely populated regions. In this study, we aim to discover such fine-scale transmission patterns via deep learning.

METHODS

We introduce the notion of TransCode to characterize fine-scale spatiotemporal transmission patterns of COVID-19 caused by metapopulation mobility and contact behaviors. First, in Hong Kong, China, we construct the mobility trajectories of confirmed cases using their visiting records. Then we estimate the transmissibility of individual cases in different locations based on their temporal infectiousness distribution. Integrating the spatial and temporal information, we represent the TransCode via spatiotemporal transmission networks. Further, we propose a deep transfer learning model to adapt the TransCode of Hong Kong, China to achieve fine-scale transmission characterization and risk prediction in six densely populated metropolises: New York City, San Francisco, Toronto, London, Berlin, and Tokyo, where fine-scale data are limited. All the data used in this study are publicly available.

RESULTS

The TransCode of Hong Kong, China derived from the spatial transmission information and temporal infectiousness distribution of individual cases reveals the transmission patterns (e.g., the imported and exported transmission intensities) at the district and constituency levels during different COVID-19 outbreaks waves. By adapting the TransCode of Hong Kong, China to other data-limited densely populated metropolises, the proposed method outperforms other representative methods by more than 10% in terms of the prediction accuracy of the disease dynamics (i.e., the trend of case numbers), and the fine-scale spatiotemporal transmission patterns in these metropolises could also be well captured due to some shared intrinsically common patterns of human mobility and contact behaviors at the metapopulation level.

CONCLUSIONS

The fine-scale transmission patterns due to the metapopulation level mobility (e.g., travel across different districts) and contact behaviors (e.g., gathering in social-economic centers) are one of the main contributors to the rapid spread of the virus. Characterization of the fine-scale transmission patterns using the TransCode will facilitate the development of tailor-made intervention strategies to effectively contain disease transmission in the targeted regions.

A model of behavioural response to risk accurately predicts the statistical distribution of COVID-19 infection and reproduction numbers

One clear aspect of behaviour in the COVID-19 pandemic has been people's focus on, and response to, reported or observed infection numbers in their community. We describe a simple model of infectious disease spread in a pandemic situation where people's behaviour is influenced by the current risk of infection and where this behavioural response acts homeostatically to return infection risk to a certain preferred level. This homeostatic response is active until approximate herd immunity is reached: in this domain the model predicts that the reproduction rate R will be centred around a median of 1, that proportional change in infection numbers will follow the standard Cauchy distribution with location and scale parameters 0 and 1, and that high infection numbers will follow a power-law frequency distribution with exponent 2. To test these predictions we used worldwide COVID-19 data from 1st February 2020 to 30th June 2022 to calculate [Formula: see text] confidence interval estimates across countries for these R, location, scale and exponent parameters. The resulting median R estimate was [Formula: see text] (predicted value 1) the proportional change location estimate was [Formula: see text] (predicted value 0), the proportional change scale estimate was [Formula: see text] (predicted value 1), and the frequency distribution exponent estimate was [Formula: see text] (predicted value 2); in each case the observed estimate agreed with model predictions.

A deconvolution approach to modelling surges in COVID-19 cases and deaths

The COVID-19 pandemic continues to emphasize the importance of epidemiological modelling in guiding timely and systematic responses to public health threats. Nonetheless, the predictive qualities of these models remain limited by their underlying assumptions of the factors and determinants shaping national and regional disease landscapes. Here, we introduce epidemiological feature detection, a novel latent variable mixture modelling approach to extracting and parameterizing distinct and localized features of real-world trends in daily COVID-19 cases and deaths. In this approach, we combine methods of peak deconvolution that are commonly used in spectroscopy with the susceptible-infected-recovered-deceased model of disease transmission. We analyze the second wave of the COVID-19 pandemic in Israel, Canada, and Germany and find that the lag time between reported cases and deaths, which we term case-death latency, is closely correlated with adjusted case fatality rates across these countries. Our findings illustrate the spatiotemporal variability of both these disease metrics within and between different disease landscapes. They also highlight the complex relationship between case-death latency, adjusted case fatality rate, and COVID-19 management across various degrees of decentralized governments and administrative structures, which provides a retrospective framework for responding to future pandemics and disease outbreaks.

Unraveling the COVID-19 hospitalization dynamics in Spain using Bayesian inference

BACKGROUND

One of the main challenges of the COVID-19 pandemic is to make sense of available, but often heterogeneous and noisy data. This contribution presents a data-driven methodology that allows exploring the hospitalization dynamics of COVID-19, exemplified with a study of 17 autonomous regions in Spain from summer 2020 to summer 2021.

METHODS

We use data on new daily cases and hospitalizations reported by the Spanish Ministry of Health to implement a Bayesian inference method that allows making short-term predictions of bed occupancy of COVID-19 patients in each of the autonomous regions of the country.

RESULTS

We show how to use the temporal series for the number of daily admissions and discharges from hospital to reproduce the hospitalization dynamics of COVID-19 patients. For the case-study of the region of Aragon, we estimate that the probability of being admitted to hospital care upon infection is 0.090 [0.086-0.094], (95% C.I.), with the distribution governing hospital admission yielding a median interval of 3.5 days and an IQR of 7 days. Likewise, the distribution on the length of stay produces estimates of 12 days for the median and 10 days for the IQR. A comparison between model parameters for the regions analyzed allows to detect differences and changes in policies of the health authorities.

CONCLUSIONS

We observe important regional differences, signaling that to properly compare very different populations, it is paramount to acknowledge all the diversity in terms of culture, socio-economic status, and resource availability. To better understand the impact of this pandemic, much more data, disaggregated and properly annotated, should be made available.

Stochastic compartmental models of the COVID-19 pandemic must have temporally correlated uncertainties

Compartmental models are an important quantitative tool in epidemiology, enabling us to forecast the course of a communicable disease. However, the model parameters, such as the infectivity rate of the disease, are riddled with uncertainties, which has motivated the development and use of stochastic compartmental models. Here, we first show that a common stochastic model, which treats the uncertainties as white noise, is fundamentally flawed since it erroneously implies that greater parameter uncertainties will lead to the eradication of the disease. Then, we present a principled modelling of the uncertainties based on reasonable assumptions on the contacts of each individual. Using the central limit theorem and Doob’s theorem on Gaussian Markov processes, we prove that the correlated Ornstein–Uhlenbeck (OU) process is the appropriate tool for modelling uncertainties in the infectivity rate. We demonstrate our results using a compartmental model of the COVID-19 pandemic and the available US data from the Johns Hopkins University COVID-19 database. In particular, we show that the white noise stochastic model systematically underestimates the severity of the Omicron variant of COVID-19, whereas the OU model correctly forecasts the course of this variant. Moreover, using an SIS model of sexually transmitted disease, we derive an exact closed-form solution for the final distribution of infected individuals. This analytical result shows that the white noise model underestimates the severity of the pandemic because of unrealistic noise-induced transitions. Our results strongly support the need for temporal correlations in modelling of uncertainties in compartmental models of infectious disease.

Mitigating the outbreak of an infectious disease over its life cycle: A diffusion-based approach

We first qualitatively divide the cycle of an infectious disease outbreak into five distinct stages by following the adoption categorization from the diffusion theory. Next, we apply a standard mechanistic model, the susceptible-infected-recovered model, to simulate a variety of transmission scenarios and to quantify the benefits of various countermeasures. In particular, we apply the specific values of the newly infected to quantitatively divide an outbreak cycle into stages. We therefore reveal diverging patterns of countermeasures in different stages. The stage is critical in determining the evolutionary characteristics of the diffusion process. Our results show that it is necessary to employ appropriate diverse strategies in different stages over the life cycle of an infectious disease outbreak. In the early stages, we need to focus on prevention, early detection, and strict countermeasure (e.g., isolation and lockdown) for controlling an epidemic. It is better safe (i.e., stricter countermeasures) than sorry (i.e., let the virus spread out). There are two reasons why we should implement responsive and strict countermeasures in the early stages. The countermeasures are very effective, and the earlier the more total infected reduction over the whole cycle. The economic and societal burden for implementing countermeasures is relatively small due to limited affected areas, and the earlier the less burden. Both reasons change to the opposite in the late stages. The strategic focuses in the late stages become more delicate and balanced for two reasons: the same countermeasures become much less effective, and the society bears a much heavier burden. Strict countermeasures may become unnecessary, and we need to think about how to live with the infectious disease.

Exploring a COVID-19 Endemic Scenario: High-Resolution Agent-Based Modeling of Multiple Variants

Our efforts as a society to combat the ongoing COVID-19 pandemic are continuously challenged by the emergence of new variants. These variants can be more infectious than existing strains and many of them are also more resistant to available vaccines. The appearance of these new variants cause new surges of infections, exacerbated by infrastructural difficulties, such as shortages of medical personnel or test kits. In this work, a high-resolution computational framework for modeling the simultaneous spread of two COVID-19 variants: a widely spread base variant and a new one, is established. The computational framework consists of a detailed database of a representative U.S. town and a high-resolution agent-based model that uses the Omicron variant as the base variant and offers flexibility in the incorporation of new variants. The results suggest that the spread of new variants can be contained with highly efficacious tests and mild loss of vaccine protection. However, the aggressiveness of the ongoing Omicron variant and the current waning vaccine immunity point to an endemic phase of COVID-19, in which multiple variants will coexist and residents continue to suffer from infections.

Expectation-Based Probabilistic Naive Approach for Forecasting Involving Optimized Parameter Estimation

This paper presents a forecasting technique based on the principle of naïve approach imposed in a probabilistic sense, thus allowing to express the prediction as the statistical expectation of known observations with a weight involving an unknown parameter. This parameter is learnt from the given data through minimization of error. The theoretical foundation is laid out, and the resulting algorithm is concisely summarized. Finally, the technique is validated on several test functions (and compared with ARIMA and Holt-Winters), special sequences and real-life covid-19 data. Favorable results are obtained in every case, and important insight about the functioning of the technique is gained.

Towards evolutionary predictions: Current promises and challenges

Evolution has traditionally been a historical and descriptive science, and predicting future evolutionary processes has long been considered impossible. However, evolutionary predictions are increasingly being developed and used in medicine, agriculture, biotechnology and conservation biology. Evolutionary predictions may be used for different purposes, such as to prepare for the future, to try and change the course of evolution or to determine how well we understand evolutionary processes. Similarly, the exact aspect of the evolved population that we want to predict may also differ. For example, we could try to predict which genotype will dominate, the fitness of the population or the extinction probability of a population. In addition, there are many uses of evolutionary predictions that may not always be recognized as such. The main goal of this review is to increase awareness of methods and data in different research fields by showing the breadth of situations in which evolutionary predictions are made. We describe how diverse evolutionary predictions share a common structure described by the predictive scope, time scale and precision. Then, by using examples ranging from SARS-CoV2 and influenza to CRISPR-based gene drives and sustainable product formation in biotechnology, we discuss the methods for predicting evolution, the factors that affect predictability and how predictions can be used to prevent evolution in undesirable directions or to promote beneficial evolution (i.e. evolutionary control). We hope that this review will stimulate collaboration between fields by establishing a common language for evolutionary predictions.

Global sensitivity analysis in epidemiological modeling

Operations researchers worldwide rely extensively on quantitative simulations to model alternative aspects of the COVID-19 pandemic. Proper uncertainty quantification and sensitivity analysis are fundamental to enrich the modeling process and communicate correctly informed insights to decision-makers. We develop a methodology to obtain insights on key uncertainty drivers, trend analysis and interaction quantification through an innovative combination of probabilistic sensitivity techniques and machine learning tools. We illustrate the approach by applying it to a representative of the family of susceptible-infectious-recovered (SIR) models recently used in the context of the COVID-19 pandemic. We focus on data of the early pandemic progression in Italy and the United States (the U.S.). We perform the analysis for both cases of correlated and uncorrelated inputs. Results show that quarantine rate and intervention time are the key uncertainty drivers, have opposite effects on the number of total infected individuals and are involved in the most relevant interactions.

Learning from the COVID-19 pandemic in Italy to advance multi-hazard disaster risk management

COVID-19 challenged all national emergency management systems worldwide overlapping with other natural hazards. We framed a 'parallel phases' Disaster Risk Management (DRM) model to overcome the limitations of the existing models when dealing with complex multi-hazard risk conditions. We supported the limitations analysing Italian Red Cross data on past and ongoing emergencies including COVID-19 and we outlined three guidelines for advancing multi-hazard DRM: (i) exploiting the low emergency intensity of slow-onset hazards for preparedness actions; (ii) increasing the internal resources and making them available for international support; (iii) implementing multi-hazard seasonal impact-based forecasts to foster the planning of anticipatory actions.

Epidemic forecasting based on mobility patterns: an approach and experimental evaluation on COVID-19 Data

During an epidemic, decision-makers in public health need accurate predictions of the future case numbers, in order to control the spread of new cases and allow efficient resource planning for hospital needs and capacities. In particular, considering that infectious diseases are spread through human-human transmissions, the analysis of spatio-temporal mobility data can play a fundamental role to enable epidemic forecasting. This paper presents the design and implementation of a predictive approach, based on spatial analysis and regressive models, to discover spatio-temporal predictive epidemic patterns from mobility and infection data. The experimental evaluation, performed on mobility and COVID-19 data collected in the city of Chicago, is aimed to assess the effectiveness of the approach in a real-world scenario. 

Modelling optimal lockdowns with waning immunity

This paper studies continuing optimal lockdowns (can also be interpreted as quarantines or self-isolation) in the long run if a disease (Covid-19) is endemic and immunity can fail, that is, the disease has SIRS dynamics. We model how disease related mortality affects the optimal choices in a dynamic general equilibrium neoclassical growth framework. An extended welfare function that incorporates loss from mortality is used. In a disease endemic steady state, without this welfare loss even if there is continuing mortality, it is not optimal to impose even a partial lockdown. We characterize how the optimal restriction and equilibrium outcomes vary with the effectiveness of the lockdown, the productivity of working from home, the rate of mortality from the disease, and failure of immunity. We provide the sufficiency conditions for economic models with SIRS dynamics with disease related mortality-a class of models which are non-convex and have endogenous discounting so that no existing results are applicable.