Age-stratified discrete compartment model of the COVID-19 epidemic with application to Switzerland.
TL;DR: An age-stratified discrete compartment model is proposed as an alternative to differential equation based S-I-R type of models that captures the highly age-dependent progression of COVID-19 and is able to describe the day-by-day advancement of an infected individual in a modern health care system.
Abstract: Compartmental models enable the analysis and prediction of an epidemic including the number of infected, hospitalized and deceased individuals in a population. They allow for computational case studies on non-pharmaceutical interventions thereby providing an important basis for policy makers. While research is ongoing on the transmission dynamics of the SARS-CoV-2 coronavirus, it is important to come up with epidemic models that can describe the main stages of the progression of the associated COVID-19 respiratory disease. We propose an age-stratified discrete compartment model as an alternative to differential equation based S-I-R type of models. The model captures the highly age-dependent progression of COVID-19 and is able to describe the day-by-day advancement of an infected individual in a modern health care system. The fully-identified model for Switzerland not only predicts the overall histories of the number of infected, hospitalized and deceased, but also the corresponding age-distributions. The model-based analysis of the outbreak reveals an average infection fatality ratio of 0.4% with a pronounced maximum of 9.5% for those aged ≥ 80 years. The predictions for different scenarios of relaxing the soft lockdown indicate a low risk of overloading the hospitals through a second wave of infections. However, there is a hidden risk of a significant increase in the total fatalities (by up to 200%) in case schools reopen with insufficient containment measures in place.
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TL;DR: In this paper, an epidemiological model on a social network that takes into account heterogeneity of the population and different vaccination strategies is proposed and studied, 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.
Abstract: 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.
50 citations
TL;DR: Five different models used to study the transmission dynamics of the SARS-Cov-2 virus in India are described and the SEIR-fansy model appeared to be a good choice with publicly available R-package and desired flexibility plus accuracy.
Abstract: 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). 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. 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. 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.
27 citations
TL;DR: In this article , the authors evaluated the effectiveness of measures implemented in the school setting to safely reopen schools, or keep schools open, or both, during the COVID-19 pandemic.
Abstract: 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.
22 citations
TL;DR: In this paper, a severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) PCR diagnostics platform was established to compare different commercial and in-house RT-PCR protocols.
17 citations
02 Mar 2021
TL;DR: In this paper, a new discrete 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.
Abstract: 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.
11 citations
References
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TL;DR: During the first 2 months of the current outbreak, Covid-19 spread rapidly throughout China and caused varying degrees of illness, and patients often presented without fever, and many did not have abnormal radiologic findings.
Abstract: Background Since December 2019, when coronavirus disease 2019 (Covid-19) emerged in Wuhan city and rapidly spread throughout China, data have been needed on the clinical characteristics of...
22,622 citations
TL;DR: There is evidence that human-to-human transmission has occurred among close contacts since the middle of December 2019 and considerable efforts to reduce transmission will be required to control outbreaks if similar dynamics apply elsewhere.
Abstract: Background The initial cases of novel coronavirus (2019-nCoV)–infected pneumonia (NCIP) occurred in Wuhan, Hubei Province, China, in December 2019 and January 2020. We analyzed data on the...
13,101 citations
TL;DR: Threshold theorems involving the basic reproduction number, the contact number, and the replacement number $R$ are reviewed for classic SIR epidemic and endemic models and results with new expressions for $R_{0}$ are obtained for MSEIR and SEIR endemic models with either continuous age or age groups.
Abstract: Many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases. Threshold theorems involving the basic reproduction number $R_{0}$, the contact number $\sigma$, and the replacement number $R$ are reviewed for the classic SIR epidemic and endemic models. Similar results with new expressions for $R_{0}$ are obtained for MSEIR and SEIR endemic models with either continuous age or age groups. Values of $R_{0}$ and $\sigma$ are estimated for various diseases including measles in Niger and pertussis in the United States. Previous models with age structure, heterogeneity, and spatial structure are surveyed.
5,915 citations
TL;DR: It is inferred that epidemics are already growing exponentially in multiple major cities of China with a lag time behind the Wuhan outbreak of about 1–2 weeks, and that other major Chinese cities are probably sustaining localised outbreaks.
3,938 citations
TL;DR: It is shown that in certain special cases one can easily compute or estimate the expected number of secondary cases produced by a typical infected individual during its entire period of infectiousness in a completely susceptible population.
Abstract: The expected number of secondary cases produced by a typical infected individual during its entire period of infectiousness in a completely susceptible population is mathematically defined as the dominant eigenvalue of a positive linear operator. It is shown that in certain special cases one can easily compute or estimate this eigenvalue. Several examples involving various structuring variables like age, sexual disposition and activity are presented.
3,885 citations