COVID-19 outbreak in Wuhan demonstrates the limitations of publicly available case numbers for epidemiological modeling

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.

Long-term monitoring of SARS-CoV-2 seroprevalence and variants in Ethiopia provides prediction for immunity and cross-immunity

Under-reporting of COVID-19 and the limited information about circulating SARS-CoV-2 variants remain major challenges for many African countries. We analyzed SARS-CoV-2 infection dynamics in Addis Ababa and Jimma, Ethiopia, focusing on reinfection, immunity, and vaccination effects. We conducted an antibody serology study spanning August 2020 to July 2022 with five rounds of data collection across a population of 4723, sequenced PCR-test positive samples, used available test positivity rates, and constructed two mathematical models integrating this data. A multivariant model explores variant dynamics identifying wildtype, alpha, delta, and omicron BA.4/5 as key variants in the study population, and cross-immunity between variants, revealing risk reductions between 24% and 69%. An antibody-level model predicts slow decay leading to sustained high antibody levels. Retrospectively, increased early vaccination might have substantially reduced infections during the delta and omicron waves in the considered group of individuals, though further vaccination now seems less impactful.

Modeling county level COVID-19 transmission in the greater St. Louis area: Challenges of uncertainty and identifiability when fitting mechanistic models to time-varying processes

We use a compartmental model with a time-varying transmission parameter to describe county level COVID-19 transmission in the greater St. Louis area of Missouri and investigate the challenges in fitting such a model to time-varying processes. We fit this model to synthetic and real confirmed case and hospital discharge data from May to December 2020 and calculate uncertainties in the resulting parameter estimates. We also explore non-identifiability within the estimated parameter set. We find that the death rate of infectious non-hospitalized individuals, the testing parameter and the initial number of exposed individuals are not identifiable based on an investigation of correlation coefficients between pairs of parameter estimates. We also explore how this non-identifiability ties back into uncertainties in the estimated parameters and find that it inflates uncertainty in the estimates of our time-varying transmission parameter. However, we do find that R0 is not highly affected by non-identifiability of its constituent components and the uncertainties associated with the quantity are smaller than those of the estimated parameters. Parameter values estimated from data will always be associated with some uncertainty and our work highlights the importance of conducting these analyses when fitting such models to real data. Exploring identifiability and uncertainty is crucial in revealing how much we can trust the parameter estimates.

Susceptible-Infected-Susceptible type COVID-19 spread with collective effects

Many models developed to forecast and attempt to understand the COVID-19 pandemic are highly complex, and few take collective behavior into account. As the pandemic progressed individual recurrent infection was observed and simpler susceptible-infected type models were introduced. However, these do not include mechanisms to model collective behavior. Here, we introduce an extension of the SIS model that accounts for collective behavior and show that it has four equilibria. Two of the equilibria are the standard SIS model equilibria, a third is always unstable, and a fourth where collective behavior and infection prevalence interact to produce either node-like or oscillatory dynamics. We then parameterized the model using estimates of the transmission and recovery rates for COVID-19 and present phase diagrams for fixed recovery rate and free transmission rate, and both rates fixed. We observe that regions of oscillatory dynamics exist in both cases and that the collective behavior parameter regulates their extent. Finally, we show that the system exhibits hysteresis when the collective behavior parameter varies over time. This model provides a minimal framework for explaining oscillatory phenomena such as recurring waves of infection and hysteresis effects observed in COVID-19, and other SIS-type epidemics, in terms of collective behavior.

How to model the impact of vaccines for policymaking when the characteristics are uncertain: A case study in Thailand prior to the vaccine rollout during the COVID-19 pandemic

Thailand faced a dilemma of which groups to prioritise with a limited first tranche of COVID-19 vaccinations in early 2021, at a time when there was low incidence and low mortality in the country. A mathematical modelling analysis was performed to compare the potential short-term impact of allocating the available doses to either the high severity group (over 65-year-olds) or the high transmission group (aged 20-39). At the time of the analysis, there was uncertainty about the precise characteristics of the vaccines available, in terms of their potential impact on transmission and reductions to the severity of infection. As such, a range of vaccine characteristic scenarios, with differing levels of severity and transmission reductions were explored. Using the evidence available at the time regarding severity reduction of infection due to the vaccines, the model suggested that vaccinating high severity group should be the priority if reductions in deaths is the priority. Vaccinating this group was found to have a direct impact on reducing the number of deaths, while the incidence and hospitalisations remained unchanged. However, the model found that vaccinating the high transmission group with a vaccine with sufficiently high protection against infection (more than 70%) could provide enough herd effects to delay the expected epidemic peak, resulting in both case and death reductions in both target groups. The model explored a 12-month time horizon. These analyses helped to inform the vaccination strategy in Thailand throughout 2021 and can inform future modelling studies for policymaking when the characteristics of vaccines are uncertain.

An age-of-infection model with both symptomatic and asymptomatic infections

We formulate a general age-of-infection epidemic model with two pathways: the symptomatic infections and the asymptomatic infections. We then calculate the basic reproduction number [Formula: see text] and establish the final size relation. It is shown that the ratio of accumulated counts of symptomatic patients and asymptomatic patients is determined by the symptomatic ratio f which is defined as the probability of eventually becoming symptomatic after being infected. We also formulate and study a general age-of-infection model with disease deaths and with two infection pathways. The final size relation is investigated, and the upper and lower bounds for final epidemic size are given. Several numerical simulations are performed to verify the analytical results.

Integrative modelling of reported case numbers and seroprevalence reveals time-dependent test efficiency and infectious contacts

Mathematical models have been widely used during the ongoing SARS-CoV-2 pandemic for data interpretation, forecasting, and policy making. However, most models are based on officially reported case numbers, which depend on test availability and test strategies. The time dependence of these factors renders interpretation difficult and might even result in estimation biases. Here, we present a computational modelling framework that allows for the integration of reported case numbers with seroprevalence estimates obtained from representative population cohorts. To account for the time dependence of infection and testing rates, we embed flexible splines in an epidemiological model. The parameters of these splines are estimated, along with the other parameters, from the available data using a Bayesian approach. The application of this approach to the official case numbers reported for Munich (Germany) and the seroprevalence reported by the prospective COVID-19 Cohort Munich (KoCo19) provides first estimates for the time dependence of the under-reporting factor. Furthermore, we estimate how the effectiveness of non-pharmaceutical interventions and of the testing strategy evolves over time. Overall, our results show that the integration of temporally highly resolved and representative data is beneficial for accurate epidemiological analyses.

Monitoring COVID-19 in Colombia during the first year of the pandemic

Background:

COVID-19 cases in Medellín, the second largest city in Colombia, were monitored during the first year of the pandemic using both mathematical models based on transmission theory and surveillance from each observed epidemic phase.

Design and Methods:

Expected cases were estimated using mandatory reporting data from Colombia’s national epidemiological surveillance system from March 7, 2020 to March 7, 2021. Initially, the range of daily expected cases was estimated using a Borel-Tanner stochastic model and a deterministic Susceptible-Infected-Removed (SIR) model. A subsequent expanded version of the SIR model was used to include asymptomatic cases, severe cases and deaths. The moving average, standard deviation, and goodness of fit of estimated cases relative to confirmed reported cases were assessed, and local transmission in Medellin was contrasted with national transmission in Colombia.

Results:

The initial phase was characterized by imported case detection and the later phase by community transmission and increases in case magnitude and severity. In the initial phase, a maximum range of expected cases was obtained based on the stochastic model, which even accounted for the reduction of new imported cases following the closure of international airports. The deterministic estimate achieved an adequate fit with respect to accumulated cases until the conclusion of the mandatory national quarantine and gradual reopening, when reported cases increased. The estimated new cases were reasonably fit with the maximum reported incidence.

Conclusion:

Adequate model fit was obtained with the reported data. This experience of monitoring epidemic trajectory can be extended using models adapted to local conditions.

Compartmental structures used in modeling COVID-19: a scoping review

Background

The coronavirus disease 2019 (COVID-19) epidemic, considered as the worst global public health event in nearly a century, has severely affected more than 200 countries and regions around the world. To effectively prevent and control the epidemic, researchers have widely employed dynamic models to predict and simulate the epidemic’s development, understand the spread rule, evaluate the effects of intervention measures, inform vaccination strategies, and assist in the formulation of prevention and control measures. In this review, we aimed to sort out the compartmental structures used in COVID-19 dynamic models and provide reference for the dynamic modeling for COVID-19 and other infectious diseases in the future.

Main text

A scoping review on the compartmental structures used in modeling COVID-19 was conducted. In this scoping review, 241 research articles published before May 14, 2021 were analyzed to better understand the model types and compartmental structures used in modeling COVID-19. Three types of dynamics models were analyzed: compartment models expanded based on susceptible-exposed-infected-recovered (SEIR) model, meta-population models, and agent-based models. The expanded compartments based on SEIR model are mainly according to the COVID-19 transmission characteristics, public health interventions, and age structure. The meta-population models and the agent-based models, as a trade-off for more complex model structures, basic susceptible-exposed-infected-recovered or simply expanded compartmental structures were generally adopted.

Conclusion

There has been a great deal of models to understand the spread of COVID-19, and to help prevention and control strategies. Researchers build compartments according to actual situation, research objectives and complexity of models used. As the COVID-19 epidemic remains uncertain and poses a major challenge to humans, researchers still need dynamic models as the main tool to predict dynamics, evaluate intervention effects, and provide scientific evidence for the development of prevention and control strategies. The compartmental structures reviewed in this study provide guidance for future modeling for COVID-19, and also offer recommendations for the dynamic modeling of other infectious diseases.

Graphical Abstract

Supplementary Information

The online version contains supplementary material available at 10.1186/s40249-022-01001-y.

Structural identifiability and observability of compartmental models of the COVID-19 pandemic

The recent coronavirus disease (COVID-19) outbreak has dramatically increased the public awareness and appreciation of the utility of dynamic models. At the same time, the dissemination of contradictory model predictions has highlighted their limitations. If some parameters and/or state variables of a model cannot be determined from output measurements, its ability to yield correct insights - as well as the possibility of controlling the system - may be compromised. Epidemic dynamics are commonly analysed using compartmental models, and many variations of such models have been used for analysing and predicting the evolution of the COVID-19 pandemic. In this paper we survey the different models proposed in the literature, assembling a list of 36 model structures and assessing their ability to provide reliable information. We address the problem using the control theoretic concepts of structural identifiability and observability. Since some parameters can vary during the course of an epidemic, we consider both the constant and time-varying parameter assumptions. We analyse the structural identifiability and observability of all of the models, considering all plausible choices of outputs and time-varying parameters, which leads us to analyse 255 different model versions. We classify the models according to their structural identifiability and observability under the different assumptions and discuss the implications of the results. We also illustrate with an example several alternative ways of remedying the lack of observability of a model. Our analyses provide guidelines for choosing the most informative model for each purpose, taking into account the available knowledge and measurements.