Age-stratified discrete compartment model of the COVID-19 epidemic with application to Switzerland

Projection of healthcare demand in Germany and Switzerland urged by Omicron wave (January-March 2022)

In January 2022, after the implementation of broad vaccination programs, the Omicron wave was propagating across Europe. There was an urgent need to understand how population immunity affects the dynamics of the COVID-19 pandemic when the loss of vaccine protection was concurrent with the emergence of a new variant of concern. In particular, assessing the risk of saturation of the healthcare systems was crucial to manage the pandemic and allow a transition towards the endemic course of SARS-CoV-2 by implementing more refined mitigation strategies that shield the most vulnerable groups and protect the healthcare systems. We investigated the epidemic dynamics by means of compartmental models that describe the age-stratified social-mixing and consider vaccination status, type, and waning of the efficacy. In response to the acute situation, our model aimed at (i) providing insight into the plausible scenarios that were likely to occur in Switzerland and Germany in the midst of the Omicron wave, (ii) informing public health authorities, and (iii) helping take informed decisions to minimize negative consequences of the pandemic. Despite the unprecedented numbers of new positive cases, our results suggested that, in all plausible scenarios, the wave was unlikely to create an overwhelming healthcare demand; due to the lower hospitalization rate and the effectiveness of the vaccines in preventing a severe course of the disease. This prediction came true and the healthcare systems in Switzerland and Germany were not pushed to the limit, despite the unprecedentedly large number of infections. By retrospective comparison of the model predictions with the official reported data of the epidemic dynamic, we demonstrate the ability of the model to capture the main features of the epidemic dynamic and the corresponding healthcare demand. In a broader context, our framework can be applied also to endemic scenarios, offering quantitative support for refined public health interventions in response to recurring waves of COVID-19 or other infectious diseases.

Novel model prediction time-to-event analysis: data validation and estimation of 200 million cases in the global COVID-19 epidemic

OBJECTIVES

Assessment of recuperation and death times of a population inflicted by an epidemic has only been feasible through studying a sample of individuals via time-to-event analysis, which requires identified participants. Therefore, we aimed to introduce an original model to estimate the average recovery/death times of infected population of contagious diseases without the need to undertake survival analysis and just through the data of unidentified infected, recovered and dead cases.

DESIGN

Cross-sectional study.

SETTING

An internet source that asserted from official sources of each government. The model includes two techniques-curve fitting and optimisation problems. First, in the curve fitting process, the data of the three classes are simultaneously fitted to functions with defined constraints to derive the average times. In the optimisation problems, data are directly fed to the technique to achieve the average times. Further, the model is applied to the available data of COVID-19 of 200 million people throughout the globe.

RESULTS

The average times obtained by the two techniques indicated conformity with one another showing p values of 0.69, 0.51, 0.48 and 0.13 with one, two, three and four surges in our timespan, respectively. Two types of irregularity are detectable in the data, significant difference between the infected population and the sum of the recovered and deceased population (discrepancy) and abrupt increase in the cumulative distributions (step). Two indices, discrepancy index (DI) and error of fit index (EI), are developed to quantify these irregularities and correlate them with the conformity of the time averages obtained by the two techniques. The correlations between DI and EI and the quantified conformity of the results were -0.74 and -0.93, respectively.

CONCLUSION

The results of statistical analyses point out that the proposed model is suitable to estimate the average times between recovery and death.

Data-driven multiscale dynamical framework to control a pandemic evolution with non-pharmaceutical interventions

Before the availability of vaccines, many countries have resorted multiple times to drastic social restrictions to prevent saturation of their health care system, and to regain control over an otherwise exponentially increasing COVID-19 pandemic. With the advent of data-sharing, computational approaches are key to efficiently control a pandemic with non-pharmaceutical interventions (NPIs). Here we develop a data-driven computational framework based on a time discrete and age-stratified compartmental model to control a pandemic evolution inside and outside hospitals in a constantly changing environment with NPIs. Besides the calendrical time, we introduce a second time-scale for the infection history, which allows for non-exponential transition probabilities. We develop inference methods and feedback procedures to successively recalibrate model parameters as new data becomes available. As a showcase, we calibrate the framework to study the pandemic evolution inside and outside hospitals in France until February 2021. We combine national hospitalization statistics from governmental websites with clinical data from a single hospital to calibrate hospitalization parameters. We infer changes in social contact matrices as a function of NPIs from positive testing and new hospitalization data. We use simulations to infer hidden pandemic properties such as the fraction of infected population, the hospitalisation probability, or the infection fatality ratio. We show how reproduction numbers and herd immunity levels depend on the underlying social dynamics.

Model-Based Analysis of SARS-CoV-2 Infections, Hospitalization and Outcome in Germany, the Federal States and Districts

The coronavirus disease 2019 (COVID-19) pandemic challenged many national health care systems, with hospitals reaching capacity limits of intensive care units (ICU). Thus, the estimation of acute local burden of ICUs is critical for appropriate management of health care resources. In this work, we applied non-linear mixed effects modeling to develop an epidemiological SARS-CoV-2 infection model for Germany, with its 16 federal states and 400 districts, that describes infections as well as COVID-19 inpatients, ICU patients with and without mechanical ventilation, recoveries, and fatalities during the first two waves of the pandemic until April 2021. Based on model analyses, covariates influencing the relation between infections and outcomes were explored. Non-pharmaceutical interventions imposed by governments were found to have a major impact on the spreading of SARS-CoV-2. Patient age and sex, the spread of variant B.1.1.7, and the testing strategy (number of tests performed weekly, rate of positive tests) affected the severity and outcome of recorded cases and could reduce the observed unexplained variability between the states. Modeling could reasonably link the discrepancies between fine-grained model simulations of the 400 German districts and the reported number of available ICU beds to coarse-grained COVID-19 patient distribution patterns within German regions.

Using simulation modelling and systems science to help contain COVID-19: A systematic review

This study systematically reviews applications of three simulation approaches, that is, system dynamics model (SDM), agent-based model (ABM) and discrete event simulation (DES), and their hybrids in COVID-19 research and identifies theoretical and application innovations in public health. Among the 372 eligible papers, 72 focused on COVID-19 transmission dynamics, 204 evaluated both pharmaceutical and non-pharmaceutical interventions, 29 focused on the prediction of the pandemic and 67 investigated the impacts of COVID-19. ABM was used in 275 papers, followed by 54 SDM papers, 32 DES papers and 11 hybrid model papers. Evaluation and design of intervention scenarios are the most widely addressed area accounting for 55% of the four main categories, that is, the transmission of COVID-19, prediction of the pandemic, evaluation and design of intervention scenarios and societal impact assessment. The complexities in impact evaluation and intervention design demand hybrid simulation models that can simultaneously capture micro and macro aspects of the socio-economic systems involved.

Modeling the initial phase of COVID-19 epidemic: The role of age and disease severity in the Basque Country, Spain

Declared a pandemic by the World Health Organization (WHO), COVID-19 has spread rapidly around the globe. With eventually substantial global underestimation of infection, by the end of March 2022, more than 470 million cases were confirmed, counting more than 6.1 million deaths worldwide. COVID-19 symptoms range from mild (or no) symptoms to severe illness, with disease severity and death occurring according to a hierarchy of risks, with age and pre-existing health conditions enhancing risks of disease severity. In order to understand the dynamics of disease severity during the initial phase of the pandemic, we propose a modeling framework stratifying the studied population into two groups, older and younger, assuming different risks for severe disease manifestation. The deterministic and the stochastic models are parametrized using epidemiological data for the Basque Country population referring to confirmed cases, hospitalizations and deaths, from February to the end of March 2020. Using similar parameter values, both models were able to describe well the existing data. A detailed sensitivity analysis was performed to identify the key parameters influencing the transmission dynamics of COVID-19 in the population. We observed that the population younger than 60 years old of age would contribute more to the overall force of infection than the older population, as opposed to the already existing age-structured models, opening new ways to understand the effect of population age on disease severity during the COVID-19 pandemic. With mild/asymptomatic cases significantly influencing the disease spreading and control, our findings support the vaccination strategy prioritising the most vulnerable individuals to reduce hospitalization and deaths, as well as the non-pharmaceutical intervention measures to reduce disease transmission.

Assessing the risk of pandemic outbreaks across municipalities with mathematical descriptors based on age and mobility restrictions

By March 14th 2022, Spain is suffering the sixth wave of the COVID-19 pandemic. All the previous waves have been intimately related to the degree of imposed mobility restrictions and its consequent release. Certain factors explain the incidence of the virus across regions revealing the weak locations that probably require some medical reinforcements. The most relevant ones relate with mobility restrictions by age and administrative competence, i.e., spatial constrains. In this work, we aim to find a mathematical descriptor that could identify the critical communities that are more likely to suffer pandemic outbreaks and, at the same time, to estimate the impact of different mobility restrictions. We analyze the incidence of the virus in combination with mobility flows during the so-called second wave (roughly from August 1st to November 30th, 2020) using a SEIR compartmental model. After that, we derive a mathematical descriptor based on linear stability theory that quantifies the potential impact of becoming a hotspot. Once the model is validated, we consider different confinement scenarios and containment protocols aimed to control the virus spreading. The main findings from our simulations suggest that the confinement of the economically non-active individuals may result in a significant reduction of risk, whose effects are equivalent to the confinement of the total population. This study is conducted across the totality of municipalities in Spain.

Effective mathematical modelling of health passes during a pandemic

We study the impact on the epidemiological dynamics of a class of restrictive measures that are aimed at reducing the number of contacts of individuals who have a higher risk of being infected with a transmittable disease. Such measures are currently either implemented or at least discussed in numerous countries worldwide to ward off a potential new wave of COVID-19. They come in the form of Health Passes (HP), which grant full access to public life only to individuals with a certificate that proves that they have either been fully vaccinated, have recovered from a previous infection or have recently tested negative to SARS-Cov-2. We develop both a compartmental model as well as an epidemic Renormalisation Group approach, which is capable of describing the dynamics over a longer period of time, notably an entire epidemiological wave. Introducing different versions of HPs in this model, we are capable of providing quantitative estimates on the effectiveness of the underlying measures as a function of the fraction of the population that is vaccinated and the vaccination rate. We apply our models to the latest COVID-19 wave in several European countries, notably Germany and Austria, which validate our theoretical findings.

A hybrid Neural Network-SEIR model for forecasting intensive care occupancy in Switzerland during COVID-19 epidemics

Anticipating intensive care unit (ICU) occupancy is critical in supporting decision makers to impose (or relax) measures that mitigate COVID-19 transmission. Mechanistic approaches such as Susceptible-Infected-Recovered (SIR) models have traditionally been used to achieve this objective. However, formulating such models is challenged by the necessity to formulate equations for plausible causal mechanisms between the intensity of COVID-19 transmission and external epidemic drivers such as temperature, and the stringency of non-pharmaceutical interventions. Here, we combined a neural network model (NN) with a Susceptible-Exposed-Infected-Recovered model (SEIR) in a hybrid model and attempted to increase the prediction accuracy of existing models used to forecast ICU occupancy. Between 1st of October, 2020 - 1st of July, 2021, the hybrid model improved performances of the SEIR model at different geographical levels. At a national level, the hybrid model improved, prediction accuracy (i.e., mean absolute error) by 74%. At the cantonal and hospital levels, the reduction on the forecast's mean absolute error were 46% and 50%, respectively. Our findings illustrate those predictions from hybrid model can be used to anticipate occupancy in ICU, and support the decision-making for lifesaving actions such as the transfer of patients and dispatching of medical personnel and ventilators.

Intensive care unit occupancy predictions in the COVID-19 pandemic based on age-structured modelling and differential flatness

The COVID-19 pandemic confronts governments and their health systems with great challenges for disease management. In many countries, hospitalization and in particular ICU occupancy is the primary measure for policy makers to decide on possible non-pharmaceutical interventions. In this paper a combined methodology for the prediction of COVID-19 case numbers, case-specific hospitalization and ICU admission rates as well as hospital and ICU occupancies is proposed. To this end, we employ differential flatness to provide estimates of the states of an epidemiological compartmental model and estimates of the unknown exogenous inputs driving its nonlinear dynamics. A main advantage of this method is that it requires the reported infection cases as the only data source. As vaccination rates and case-specific ICU rates are both strongly age-dependent, specifically an age-structured compartmental model is proposed to estimate and predict the spread of the epidemic across different age groups. By utilizing these predictions, case-specific hospitalization and case-specific ICU rates are subsequently estimated using deconvolution techniques. In an analysis of various countries we demonstrate how the methodology is able to produce real-time state estimates and hospital/ICU occupancy predictions for several weeks thus providing a sound basis for policy makers.

Measures implemented in the school setting to contain the COVID-19 pandemic

BACKGROUND

In response to the spread of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and the impact of coronavirus disease 2019 (COVID-19), governments have implemented a variety of measures to control the spread of the virus and the associated disease. Among these, have been measures to control the pandemic in primary and secondary school settings.

OBJECTIVES

To assess the effectiveness of measures implemented in the school setting to safely reopen schools, or keep schools open, or both, during the COVID-19 pandemic, with particular focus on the different types of measures implemented in school settings and the outcomes used to measure their impacts on transmission-related outcomes, healthcare utilisation outcomes, other health outcomes as well as societal, economic, and ecological outcomes.  SEARCH METHODS: We searched the Cochrane Central Register of Controlled Trials (CENTRAL), MEDLINE, Embase, and the Educational Resources Information Center, as well as COVID-19-specific databases, including the Cochrane COVID-19 Study Register and the WHO COVID-19 Global literature on coronavirus disease (indexing preprints) on 9 December 2020. We conducted backward-citation searches with existing reviews.

SELECTION CRITERIA

We considered experimental (i.e. randomised controlled trials; RCTs), quasi-experimental, observational and modelling studies assessing the effects of measures implemented in the school setting to safely reopen schools, or keep schools open, or both, during the COVID-19 pandemic. Outcome categories were (i) transmission-related outcomes (e.g. number or proportion of cases); (ii) healthcare utilisation outcomes (e.g. number or proportion of hospitalisations); (iii) other health outcomes (e.g. physical, social and mental health); and (iv) societal, economic and ecological outcomes (e.g. costs, human resources and education). We considered studies that included any population at risk of becoming infected with SARS-CoV-2 and/or developing COVID-19 disease including students, teachers, other school staff, or members of the wider community.  DATA COLLECTION AND ANALYSIS: Two review authors independently screened titles, abstracts and full texts. One review author extracted data and critically appraised each study. One additional review author validated the extracted data. To critically appraise included studies, we used the ROBINS-I tool for quasi-experimental and observational studies, the QUADAS-2 tool for observational screening studies, and a bespoke tool for modelling studies. We synthesised findings narratively. Three review authors made an initial assessment of the certainty of evidence with GRADE, and several review authors discussed and agreed on the ratings.

MAIN RESULTS

We included 38 unique studies in the analysis, comprising 33 modelling studies, three observational studies, one quasi-experimental and one experimental study with modelling components. Measures fell into four broad categories: (i) measures reducing the opportunity for contacts; (ii) measures making contacts safer; (iii) surveillance and response measures; and (iv) multicomponent measures. As comparators, we encountered the operation of schools with no measures in place, less intense measures in place, single versus multicomponent measures in place, or closure of schools. Across all intervention categories and all study designs, very low- to low-certainty evidence ratings limit our confidence in the findings. Concerns with the quality of modelling studies related to potentially inappropriate assumptions about the model structure and input parameters, and an inadequate assessment of model uncertainty. Concerns with risk of bias in observational studies related to deviations from intended interventions or missing data. Across all categories, few studies reported on implementation or described how measures were implemented. Where we describe effects as 'positive', the direction of the point estimate of the effect favours the intervention(s); 'negative' effects do not favour the intervention.  We found 23 modelling studies assessing measures reducing the opportunity for contacts (i.e. alternating attendance, reduced class size). Most of these studies assessed transmission and healthcare utilisation outcomes, and all of these studies showed a reduction in transmission (e.g. a reduction in the number or proportion of cases, reproduction number) and healthcare utilisation (i.e. fewer hospitalisations) and mixed or negative effects on societal, economic and ecological outcomes (i.e. fewer number of days spent in school). We identified 11 modelling studies and two observational studies assessing measures making contacts safer (i.e. mask wearing, cleaning, handwashing, ventilation). Five studies assessed the impact of combined measures to make contacts safer. They assessed transmission-related, healthcare utilisation, other health, and societal, economic and ecological outcomes. Most of these studies showed a reduction in transmission, and a reduction in hospitalisations; however, studies showed mixed or negative effects on societal, economic and ecological outcomes (i.e. fewer number of days spent in school). We identified 13 modelling studies and one observational study assessing surveillance and response measures, including testing and isolation, and symptomatic screening and isolation. Twelve studies focused on mass testing and isolation measures, while two looked specifically at symptom-based screening and isolation. Outcomes included transmission, healthcare utilisation, other health, and societal, economic and ecological outcomes. Most of these studies showed effects in favour of the intervention in terms of reductions in transmission and hospitalisations, however some showed mixed or negative effects on societal, economic and ecological outcomes (e.g. fewer number of days spent in school). We found three studies that reported outcomes relating to multicomponent measures, where it was not possible to disaggregate the effects of each individual intervention, including one modelling, one observational and one quasi-experimental study. These studies employed interventions, such as physical distancing, modification of school activities, testing, and exemption of high-risk students, using measures such as hand hygiene and mask wearing. Most of these studies showed a reduction in transmission, however some showed mixed or no effects.   As the majority of studies included in the review were modelling studies, there was a lack of empirical, real-world data, which meant that there were very little data on the actual implementation of interventions.

AUTHORS' CONCLUSIONS

Our review suggests that a broad range of measures implemented in the school setting can have positive impacts on the transmission of SARS-CoV-2, and on healthcare utilisation outcomes related to COVID-19. The certainty of the evidence for most intervention-outcome combinations is very low, and the true effects of these measures are likely to be substantially different from those reported here. Measures implemented in the school setting may limit the number or proportion of cases and deaths, and may delay the progression of the pandemic. However, they may also lead to negative unintended consequences, such as fewer days spent in school (beyond those intended by the intervention). Further, most studies assessed the effects of a combination of interventions, which could not be disentangled to estimate their specific effects. Studies assessing measures to reduce contacts and to make contacts safer consistently predicted positive effects on transmission and healthcare utilisation, but may reduce the number of days students spent at school. Studies assessing surveillance and response measures predicted reductions in hospitalisations and school days missed due to infection or quarantine, however, there was mixed evidence on resources needed for surveillance. Evidence on multicomponent measures was mixed, mostly due to comparators. The magnitude of effects depends on multiple factors. New studies published since the original search date might heavily influence the overall conclusions and interpretation of findings for this review.

Two-Age-Structured COVID-19 Epidemic Model: Estimation of Virulence Parameters to Interpret Effects of National and Regional Feedback Interventions and Vaccination

The COVID-19 epidemic has recently led in Italy to the implementation of different external strategies in order to limit the spread of the disease in response to its transmission rate: strict national lockdown rules, followed first by a weakening of the social distancing and contact reduction feedback interventions and finally the implementation of coordinated intermittent regional actions, up to the application, in this last context, of an age-stratified vaccine prioritization strategy. This paper originally aims at identifying, starting from the available age-structured real data at the national level during the specific aforementioned scenarios, external-scenario-dependent sets of virulence parameters for a two-age-structured COVID-19 epidemic compartmental model, in order to provide an interpretation of how each external scenario modifies the age-dependent patterns of social contacts and the spread of COVID-19.

Adaptively temporal graph convolution model for epidemic prediction of multiple age groups

Introduction

Multivariate time series prediction of infectious diseases is significant to public health, and the deep learning method has attracted increasing attention in this research field.

Material and methods

An adaptively temporal graph convolution (ATGCN) model, which learns the contact patterns of multiple age groups in a graph-based approach, was proposed for COVID- 19 and influenza prediction. We compared ATGCN with autoregressive models, deep sequence learning models, and experience- based ATGCN models in short-term and long-term prediction tasks.

Results

Results showed that the ATGCN model performed better than the autoregressive models and the deep sequence learning models on two datasets in both short-term (12.5% and 10% improvements on RMSE) and long-term (12.4% and 5% improvements on RMSE) prediction tasks. And the RMSE of ATGCN predictions fluctuated least in different age groups of COVID- 19 (0.029 ± 0.003) and influenza (0.059±0.008). Compared with the Ones-ATGCN model or the Pre-ATGCN model, the ATGCN model was more robust in performance, with RMSE of 0.0293 and 0.06 on two datasets when horizon is one.

Discussion

Our research indicates a broad application prospect of deep learning in the field of infectious disease prediction. Transmission characteristics and domain knowledge of infectious diseases should be further applied to the design of deep learning models and feature selection.

Conclusion

The ATGCN model addressed the multivariate time series forecasting in a graph-based deep learning approach and achieved robust prediction on the confirmed cases of multiple age groups, indicating its great potentials for exploring the implicit interactions of multivariate variables.

Is increased mortality by multiple exposures to COVID-19 an overseen factor when aiming for herd immunity?

BACKGROUND

Governments across the globe responded with different strategies to the COVID-19 pandemic. While some countries adopted measures, which have been perceived controversial, others pursued a strategy aiming for herd immunity. The latter is even more controversial and has been called unethical by the WHO Director-General. Inevitably, without proper control measures, viral diversity increases and multiple infectious exposures become common, when the pandemic reaches its maximum. This harbors not only a potential threat overseen by simplified theoretical arguments in support of herd immunity, but also deserves attention when assessing response measures to increasing numbers of infection.

METHODS AND FINDINGS

We extend the simulation model underlying the pandemic preparedness web interface CovidSim 1.1 (http://covidsim.eu/) to study the hypothetical effect of increased morbidity and mortality due to 'multi-infections', either acquired at by successive infective contacts during the course of one infection or by a single infective contact with a multi-infected individual. The simulations are adjusted to reflect roughly the situation in the USA. We assume a phase of general contact reduction ("lockdown") at the beginning of the epidemic and additional case-isolation measures. We study the hypothetical effects of varying enhancements in morbidity and mortality, different likelihoods of multi-infected individuals to spread multi-infections and different susceptibility to multi-infections in different disease phases. It is demonstrated that multi-infections lead to a slight reduction in the number of infections, as these are more likely to get isolated due to their higher morbidity. However, the latter substantially increases the number of deaths. Furthermore, simulations indicate that a potential second lockdown can substantially decrease the epidemic peak, the number of multi-infections and deaths.

CONCLUSIONS

Enhanced morbidity and mortality due to multiple disease exposure is a potential threat in the COVID-19 pandemic that deserves more attention. Particularly it underlines another facet questioning disease management strategies aiming for herd immunity.

Socio-demographic and health factors drive the epidemic progression and should guide vaccination strategies for best COVID-19 containment

We propose and study an epidemiological model on a social network that takes into account heterogeneity of the population and different vaccination strategies. In particular, we study how the COVID-19 epidemics evolves and how it is contained by different vaccination scenarios by taking into account data showing that older people, as well as individuals with comorbidities and poor metabolic health, and people coming from economically depressed areas with lower quality of life in general, are more likely to develop severe COVID-19 symptoms, and quicker loss of immunity and are therefore more prone to reinfection. Our results reveal that the structure and the spatial arrangement of subpopulations are important epidemiological determinants. In a healthier society the disease spreads more rapidly but the consequences are less disastrous as in a society with more prevalent chronic comorbidities. If individuals with poor health are segregated within one community, the epidemic outcome is less favorable. Moreover, we show that, contrary to currently widely adopted vaccination policies, prioritizing elderly and other higher-risk groups is beneficial only if the supply of vaccine is high. If, however, the vaccination availability is limited, and if the demographic distribution across the social network is homogeneous, better epidemic outcomes are achieved if healthy people are vaccinated first. Only when higher-risk groups are segregated, like in elderly homes, their prioritization will lead to lower COVID-19 related deaths. Accordingly, young and healthy individuals should view vaccine uptake as not only protecting them, but perhaps even more so protecting the more vulnerable socio-demographic groups.

A Comparative Study of Real-Time RT-PCR-Based SARS-CoV-2 Detection Methods and Its Application to Human-Derived and Surface Swabbed Material

Real-time RT-PCR remains a gold standard in the detection of various viral diseases. In the coronavirus 2019 pandemic, multiple RT-PCR-based tests were developed to screen for viral infection. As an emergency response to increasing testing demand, we established a severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) PCR diagnostics platform for which we compared different commercial and in-house RT-PCR protocols. Four commercial, one customized, and one in-house RT-PCR protocols were evaluated with 92 SARS-CoV-2-positive and 92 SARS-CoV-2-negative samples. Furthermore, economical and practical characteristics of these protocols were compared. In addition, a highly sensitive digital droplet PCR (ddPCR) method was developed, and application of RT-PCR and ddPCR methods on SARS-CoV-2 environmental samples was examined. Very low limits of detection (1 or 2 viral copies/μL), high sensitivities (93.6% to 97.8%), and high specificities (98.7% to 100%) for the tested RT-PCR protocols were found. Furthermore, the feasibility of downscaling two of the commercial protocols, which could optimize testing capacity, was demonstrated. Tested commercial and customized RT-PCR detection kits show very good and comparable sensitivity and specificity, and the kits could be further optimized for use on SARS-CoV-2 viral samples derived from human and surface swabbed samples.

A comparison of five epidemiological models for transmission of SARS-CoV-2 in India

BACKGROUND

Many popular disease transmission models have helped nations respond to the COVID-19 pandemic by informing decisions about pandemic planning, resource allocation, implementation of social distancing measures, lockdowns, and other non-pharmaceutical interventions. We study how five epidemiological models forecast and assess the course of the pandemic in India: a baseline curve-fitting model, an extended SIR (eSIR) model, two extended SEIR (SAPHIRE and SEIR-fansy) models, and a semi-mechanistic Bayesian hierarchical model (ICM).

METHODS

Using COVID-19 case-recovery-death count data reported in India from March 15 to October 15 to train the models, we generate predictions from each of the five models from October 16 to December 31. To compare prediction accuracy with respect to reported cumulative and active case counts and reported cumulative death counts, we compute the symmetric mean absolute prediction error (SMAPE) for each of the five models. For reported cumulative cases and deaths, we compute Pearson's and Lin's correlation coefficients to investigate how well the projected and observed reported counts agree. We also present underreporting factors when available, and comment on uncertainty of projections from each model.

RESULTS

For active case counts, SMAPE values are 35.14% (SEIR-fansy) and 37.96% (eSIR). For cumulative case counts, SMAPE values are 6.89% (baseline), 6.59% (eSIR), 2.25% (SAPHIRE) and 2.29% (SEIR-fansy). For cumulative death counts, the SMAPE values are 4.74% (SEIR-fansy), 8.94% (eSIR) and 0.77% (ICM). Three models (SAPHIRE, SEIR-fansy and ICM) return total (sum of reported and unreported) cumulative case counts as well. We compute underreporting factors as of October 31 and note that for cumulative cases, the SEIR-fansy model yields an underreporting factor of 7.25 and ICM model yields 4.54 for the same quantity. For total (sum of reported and unreported) cumulative deaths the SEIR-fansy model reports an underreporting factor of 2.97. On October 31, we observe 8.18 million cumulative reported cases, while the projections (in millions) from the baseline model are 8.71 (95% credible interval: 8.63-8.80), while eSIR yields 8.35 (7.19-9.60), SAPHIRE returns 8.17 (7.90-8.52) and SEIR-fansy projects 8.51 (8.18-8.85) million cases. Cumulative case projections from the eSIR model have the highest uncertainty in terms of width of 95% credible intervals, followed by those from SAPHIRE, the baseline model and finally SEIR-fansy.

CONCLUSIONS

In this comparative paper, we describe five different models used to study the transmission dynamics of the SARS-Cov-2 virus in India. While simulation studies are the only gold standard way to compare the accuracy of the models, here we were uniquely poised to compare the projected case-counts against observed data on a test period. The largest variability across models is observed in predicting the "total" number of infections including reported and unreported cases (on which we have no validation data). The degree of under-reporting has been a major concern in India and is characterized in this report. Overall, the SEIR-fansy model appeared to be a good choice with publicly available R-package and desired flexibility plus accuracy.

Age-Stratified Infection Probabilities Combined With a Quarantine-Modified Model for COVID-19 Needs Assessments: Model Development Study

BACKGROUND

Classic compartmental models such as the susceptible-exposed-infectious-removed (SEIR) model all have the weakness of assuming a homogenous population, where everyone has an equal chance of getting infected and dying. Since it was identified in Hubei, China, in December 2019, COVID-19 has rapidly spread around the world and been declared a pandemic. Based on data from Hubei, infection and death distributions vary with age. To control the spread of the disease, various preventive and control measures such as community quarantine and social distancing have been widely used.

OBJECTIVE

Our aim is to develop a model where age is a factor, considering the study area's age stratification. Additionally, we want to account for the effects of quarantine on the SEIR model.

METHODS

We use the age-stratified COVID-19 infection and death distributions from Hubei, China (more than 44,672 infections as of February 11, 2020) as an estimate or proxy for a study area's infection and mortality probabilities for each age group. We then apply these probabilities to the actual age-stratified population of Quezon City, Philippines, to predict infectious individuals and deaths at peak. Testing with different countries shows the predicted number of infectious individuals skewing with the country's median age and age stratification, as expected. We added a Q parameter to the SEIR model to include the effects of quarantine (Q-SEIR).

RESULTS

The projections from the age-stratified probabilities give much lower predicted incidences of infection than the Q-SEIR model. As expected, quarantine tends to delay the peaks for both the exposed and infectious groups, and to "flatten" the curve or lower the predicted values for each compartment. These two estimates were used as a range to inform the local government's planning and response to the COVID-19 threat.

CONCLUSIONS

Age stratification combined with a quarantine-modified model has good qualitative agreement with observations on infections and death rates. That younger populations will have lower death rates due to COVID-19 is a fair expectation for a disease where most fatalities are among older adults.

On a Discrete SEIR Epidemic Model with Two-Doses Delayed Feedback Vaccination Control on the Susceptible

A new discrete susceptible-exposed-infectious-recovered (SEIR) epidemic model is presented subject to a feedback vaccination effort involving two doses. Both vaccination doses, which are subject to a non-necessarily identical effectiveness, are administrated by respecting a certain mutual delay interval, and their immunity effect is registered after a certain delay since the second dose. The delays and the efficacies of the doses are parameters, which can be fixed in the model for each concrete experimentation. The disease-free equilibrium point is characterized as well as its stability properties, while it is seen that no endemic equilibrium point exists. The exposed subpopulation is supposed to be infective eventually, under a distinct transmission rate of that of the infectious subpopulation. Some simulation examples are presented by using disease parameterizations of the COVID-19 pandemic under vaccination efforts requiring two doses.

On a Discrete SEIR Epidemic Model with Exposed Infectivity, Feedback Vaccination and Partial Delayed Re-Susceptibility

A new discrete Susceptible-Exposed-Infectious-Recovered (SEIR) epidemic model is proposed, and its properties of non-negativity and (both local and global) asymptotic stability of the solution sequence vector on the first orthant of the state-space are discussed. The calculation of the disease-free and the endemic equilibrium points is also performed. The model has the following main characteristics: (a) the exposed subpopulation is infective, as it is the infectious one, but their respective transmission rates may be distinct; (b) a feedback vaccination control law on the Susceptible is incorporated; and (c) the model is subject to delayed partial re-susceptibility in the sense that a partial immunity loss in the recovered individuals happens after a certain delay. In this way, a portion of formerly recovered individuals along a range of previous samples is incorporated again to the susceptible subpopulation. The rate of loss of partial immunity of the considered range of previous samples may be, in general, distinct for the various samples. It is found that the endemic equilibrium point is not reachable in the transmission rate range of values, which makes the disease-free one to be globally asymptotically stable. The critical transmission rate which confers to only one of the equilibrium points the property of being asymptotically stable (respectively below or beyond its value) is linked to the unity basic reproduction number and makes both equilibrium points to be coincident. In parallel, the endemic equilibrium point is reachable and globally asymptotically stable in the range for which the disease-free equilibrium point is unstable. It is also discussed the relevance of both the vaccination effort and the re-susceptibility level in the modification of the disease-free equilibrium point compared to its reached component values in their absence. The influences of the limit control gain and equilibrium re-susceptibility level in the reached endemic state are also explicitly made viewable for their interpretation from the endemic equilibrium components. Some simulation examples are tested and discussed by using disease parameterizations of COVID-19.