scholarly journals Exploring COVID-19 Daily Records of Diagnosed Cases and Fatalities Based on Simple Non-parametric Methods

2020 ◽  
Author(s):  
Hans H. Diebner ◽  
Nina Timmesfeld
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Time Lag ◽  
Case Fatality ◽  
Parametric Models ◽  
Intermediate Step ◽  
Parametric Methods ◽  
Temporal Behaviour ◽  
The Basic Reproduction Number ◽  
Non Parametric

Based on comprehensible non-parametric methods, estimates of crucial parameters that characterise the COVID-19 pandemic with a focus on the German epidemic are presented. Where appropriate, the estimates for Germany are compared with the results for six other countries (FR, IT, US, UK, ES, CH) to get an idea of the breadth of applicability and a relational understanding. Thereby, only prevalence data of daily reported new counts of diagnosed cases and fatalities provided by the ECDC are used. Where appropriate, the results are compared with conclusions drawn from using the dataset provided by the RKI. Drawing on uncertain a priori knowledge is avoided. Specifically, we present estimates for the duration from diagnosis to death being 13 days for Germany and about 2 days for Italy as the extremes. Furthermore, based on the knowledge of this time lag between diagnoses and deaths, properly delayed asymptotic as well as instantaneous fatality-case ratios are calculated having superiority compared to the commonly published case-fatality rate. The median of the time series of the instantaneous fatality-case ratio with proper delay of 13-days between cases and deaths for Germany turns out to be 0.024. Asymptotic values are presented for other countries with France ranking highest with a fatality-case ratio of almost 0.2 at its peak. The basic reproduction number, R_0, for Germany is estimated to be between 2.4 and 3.4. The uncertainty stems from uncertain knowledge of the generation time. A delay autocorrelation shows resonances at about 4 days and 7 days, where the latter resonance is at least partially attributable to the sampling process with weekly periodicity. The calculation of the basic reproduction number is based on an evaluation of cumulative numbers of cases yielding time-dependent doubling times as an intermediate step. This allows to infer to the reproduction number during the early phase of onset of the epidemic. In a second approach, the instantaneous basic reproduction number is derived from the incident (counts of new) cases and allows, in contrast to the first version, to infer to the temporal behaviour of the reproduction number during the later epidemic course. To conclude, by avoiding complicated parametric models we provide insights into basic features of the COVID-19 epidemic in an utmost transparent and comprehensible way.

scholarly journals Exploring COVID-19 Daily Records of Diagnosed Cases and Fatalities Based on Simple Non-parametric Methods

2021 ◽  
Author(s):  
Hans H. Diebner ◽  
Nina Timmesfeld
Keyword(s):  
Time Series ◽  
Basic Reproduction Number ◽  
Delay Time ◽  
Reproduction Number ◽  
Intermediate Step ◽  
Parametric Methods ◽  
Temporal Behaviour ◽  
Time Courses ◽  
The Basic Reproduction Number ◽  
Non Parametric

Based on comprehensible non-parametric methods, estimates of crucial parameters that characterise the COVID-19 pandemic with a focus on the German epidemic are presented. Where appropriate, the estimates for Germany are compared with the results for seven other countries (FR, IT, US, UK, ES, CH, BR) to get an idea of the breadth of applicability and a relational understanding. Thereby, only prevalence data of daily reported new counts of diagnosed cases and fatalities provided by the Johns Hopkins University are used. Drawing on uncertain a priori knowledge is avoided. Specifically, we present estimates resulting from delay-time correlations for the duration from diagnosis to death being 13 days for Germany and Switzerland. The delay-time correlation applied to time series from other countries exhibit less pronounced peaks suggesting high variabilities for the corresponding time-to-death durations. With respect to the German data, the two time series of new cases and fatalities exhibit a strong coherence within the frequency range of interest, which backs our findings. Furthermore, based on the knowledge of this time lag between diagnoses and deaths, properly delayed asymptotic as well as instantaneous fatality-case ratios are calculated having superiority compared to the commonly published case-fatality rate. The temporal median of the instantaneous fatality-case ratio with proper delay of 13-days between cases and deaths for Germany turns out to be 0.02. Time courses of asymptotic fatality-case ratios are presented for other countries which substantially differ during the first half of the pandemic, however, converge to a narrow range with standard deviation 0.57% and mean 2.4%. Additionally, the time courses of instantaneous fatality-case ratios with optimal delay for the 8 exemplarily chosen countries are calculated and compared by means of the temporal medians. Similarly to the asymptotic fatality-case ratios, the differences are much smaller than expected from mass media reports. The basic reproduction number, R0, for Germany is estimated to be between 2.4 and 3.4. The uncertainty stems from uncertain knowledge of the generation time. A delay autocorrelation shows resonances at about 4 days and 7 days, where the latter resonance is at least partially attributable to the sampling process with weekly periodicity. The calculation of the basic reproduction number is based on an evaluation of cumulative numbers of cases yielding time-dependent doubling times as an intermediate step. This allows to infer to the reproduction number during the early phase of onset of the epidemic. In a second approach, the instantaneous reproduction number is derived from the incident (counts of new) cases and allows, in contrast to the first version, to infer to the temporal behaviour of the reproduction number during the later epidemic course. The time course of the reproduction number is compared to an alternative control measure given by the per capita growth, which largely confirms the conclusions drawn from the reproduction number. To conclude, by avoiding complicated parametric models we provide insights into basic features of the COVID-19 epidemic in an utmost transparent and comprehensible way. The perhaps most striking insight is that the fatality-case ratios do not differ between countries as much as previously suspected.

scholarly journals SEIHCRD Model for COVID-19 spread scenarios, disease predictions and estimates the basic reproduction number, case fatality rate, hospital, and ICU beds requirement

2020 ◽  
Author(s):  
Avaneesh Singh ◽  
Manish Kumar Bajpai
Keyword(s):  
Basic Reproduction Number ◽  
Case Fatality Rate ◽  
Reproduction Number ◽  
Case Fatality ◽  
The United States ◽  
Fatality Rate ◽  
Hospital Beds ◽  
The Impact ◽  
Over Time ◽  
The Basic Reproduction Number

We have proposed a new mathematical method, SEIHCRD-Model that is an extension of the SEIR-Model adding hospitalized and critical twocompartments. SEIHCRD model has seven compartments: susceptible (S), exposed (E), infected (I), hospitalized (H), critical (C), recovered (R), and deceased or death (D), collectively termed SEIHCRD. We have studied COVID- 19 cases of six countries, where the impact of this disease in the highest are Brazil, India, Italy, Spain, the United Kingdom, and the United States. SEIHCRD model is estimating COVID-19 spread and forecasting under uncertainties, constrained by various observed data in the present manuscript. We have first collected the data for a specific period, then fit the model for death cases, got the values of some parameters from it, and then estimate the basic reproduction number over time, which is nearly equal to real data, infection rate, and recovery rate of COVID-19. We also compute the case fatality rate over time of COVID-19 most affected countries. SEIHCRD model computes two types of Case fatality rate one is CFR daily and the second one is total CFR. We analyze the spread and endpoint of COVID-19 based on these estimates. SEIHCRD model is time-dependent hence we estimate the date and magnitude of peaks of corresponding to the number of exposed cases, infected cases, hospitalized cases, critical cases, and the number of deceased cases of COVID-19 over time. SEIHCRD model has incorporated the social distancing parameter, different age groups analysis, number of ICU beds, number of hospital beds, and estimation of how much hospital beds and ICU beds are required in near future.

scholarly journals Estimation of the basic reproduction number, average incubation time, asymptomatic infection rate, and case fatality rate for COVID-19: Meta-analysis and sensitivity analysis

2020 ◽  
Author(s):  
Wenqing He ◽  
Grace Y. Yi ◽  
Yayuan Zhu
Keyword(s):  
Confidence Interval ◽  
Basic Reproduction Number ◽  
Incubation Time ◽  
Case Fatality Rate ◽  
Reproduction Number ◽  
Meta Analysis ◽  
Case Fatality ◽  
Asymptomatic Infection ◽  
Fatality Rate ◽  
The Basic Reproduction Number

AbstractThe coronavirus disease 2019 (COVID-19) has been found to be caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). However, comprehensive knowledge of COVID-19 remains incomplete and many important features are still unknown. This manuscripts conduct a meta-analysis and a sensitivity study to answer the questions: What is the basic reproduction number? How long is the incubation time of the disease on average? What portion of infections are asymptomatic? And ultimately, what is the case fatality rate? Our studies estimate the basic reproduction number to be 3.15 with the 95% interval (2.41, 3.90), the average incubation time to be 5.08 days with the 95% confidence interval (4.77, 5.39) (in day), the asymptomatic infection rate to be 46% with the 95% confidence interval (18.48%, 73.60%), and the case fatality rate to be 2.72% with 95% confidence interval (1.29%, 4.16%) where asymptomatic infections are accounted for.

scholarly journals Real-Time Estimation of the Risk of Death from Novel Coronavirus (COVID-19) Infection: Inference Using Exported Cases

2020 ◽  
Author(s):  
Sung-mok Jung ◽  
Andrei R. Akhmetzhanov ◽  
Katsuma Hayashi ◽  
Natalie M. Linton ◽  
Yichi Yang ◽  
...  
Keyword(s):  
Growth Rate ◽  
Basic Reproduction Number ◽  
Cumulative Incidence ◽  
Reproduction Number ◽  
Early Stage ◽  
Case Fatality ◽  
Primary Case ◽  
Risk Of Death ◽  
Novel Coronavirus ◽  
The Basic Reproduction Number

AbstractThe exported cases of 2019 novel coronavirus (COVID-19) infection that were confirmed outside of China provide an opportunity to estimate the cumulative incidence and confirmed case fatality risk (cCFR) in mainland China. Knowledge of the cCFR is critical to characterize the severity and understand the pandemic potential of COVID-19 in the early stage of the epidemic. Using the exponential growth rate of the incidence, the present study statistically estimated the cCFR and the basic reproduction number—the average number of secondary cases generated by a single primary case in a naïve population. We modeled epidemic growth either from a single index case with illness onset on 8 December, 2019 (Scenario 1), or using the growth rate fitted along with the other parameters (Scenario 2) based on data from 20 exported cases reported by 24 January, 2020. The cumulative incidence in China by 24 January was estimated at 6924 cases (95% CI: 4885, 9211) and 19,289 cases (95% CI: 10,901, 30,158), respectively. The latest estimated values of the cCFR were 5.3% (95% CI: 3.5%, 7.5%) for Scenario 1 and 8.4% (95% CI: 5.3%, 12.3%) for Scenario 2. The basic reproduction number was estimated to be 2.1 (95% CI: 2.0, 2.2) and 3.2 (95% CI: 2.7, 3.7) for Scenarios 1 and 2, respectively. Based on these results, we argued that the current COVID-19 epidemic has a substantial potential for causing a pandemic. The proposed approach provides insights in early risk assessment using publicly available data.

scholarly journals The first wave of the SARS-CoV-2 epidemic in Tuscany (Italy): A SI2R2D compartmental model with uncertainty evaluation

PLoS ONE ◽  
2021 ◽  
Vol 16 (4) ◽  
pp. e0250029
Author(s):  
Michela Baccini ◽  
Giulia Cereda ◽  
Cecilia Viscardi
Keyword(s):  
Basic Reproduction Number ◽  
Compartmental Model ◽  
Reproduction Number ◽  
Case Fatality ◽  
Parametric Bootstrap ◽  
Model Parameters ◽  
Fatality Rate ◽  
Epidemic Curve ◽  
Plausible Values ◽  
The Basic Reproduction Number

With the aim of studying the spread of the SARS-CoV-2 infection in the Tuscany region of Italy during the first epidemic wave (February-June 2020), we define a compartmental model that accounts for both detected and undetected infections and assumes that only notified cases can die. We estimate the infection fatality rate, the case fatality rate, and the basic reproduction number, modeled as a time-varying function, by calibrating on the cumulative daily number of observed deaths and notified infected, after fixing to plausible values the other model parameters to assure identifiability. The confidence intervals are estimated by a parametric bootstrap procedure and a Global Sensitivity Analysis is performed to assess the sensitivity of the estimates to changes in the values of the fixed parameters. According to our results, the basic reproduction number drops from an initial value of 6.055 to 0 at the end of the national lockdown, then it grows again, but remaining under 1. At the beginning of the epidemic, the case and the infection fatality rates are estimated to be 13.1% and 2.3%, respectively. Among the parameters considered as fixed, the average time from infection to recovery for the not notified infected appears to be the most impacting one on the model estimates. The probability for an infected to be notified has a relevant impact on the infection fatality rate and on the shape of the epidemic curve. This stresses the need of collecting information on these parameters to better understand the phenomenon and get reliable predictions.

scholarly journals Real-Time Estimation of the Risk of Death from Novel Coronavirus (COVID-19) Infection: Inference Using Exported Cases

2020 ◽  
Vol 9 (2) ◽  
pp. 523 ◽  
Author(s):  
Sung-mok Jung ◽  
Andrei R. Akhmetzhanov ◽  
Katsuma Hayashi ◽  
Natalie M. Linton ◽  
Yichi Yang ◽  
...  
Keyword(s):  
Growth Rate ◽  
Basic Reproduction Number ◽  
Cumulative Incidence ◽  
Reproduction Number ◽  
Early Stage ◽  
Case Fatality ◽  
Primary Case ◽  
Risk Of Death ◽  
Novel Coronavirus ◽  
The Basic Reproduction Number

The exported cases of 2019 novel coronavirus (COVID-19) infection that were confirmed outside China provide an opportunity to estimate the cumulative incidence and confirmed case fatality risk (cCFR) in mainland China. Knowledge of the cCFR is critical to characterize the severity and understand the pandemic potential of COVID-19 in the early stage of the epidemic. Using the exponential growth rate of the incidence, the present study statistically estimated the cCFR and the basic reproduction number—the average number of secondary cases generated by a single primary case in a naïve population. We modeled epidemic growth either from a single index case with illness onset on 8 December 2019 (Scenario 1), or using the growth rate fitted along with the other parameters (Scenario 2) based on data from 20 exported cases reported by 24 January 2020. The cumulative incidence in China by 24 January was estimated at 6924 cases (95% confidence interval [CI]: 4885, 9211) and 19,289 cases (95% CI: 10,901, 30,158), respectively. The latest estimated values of the cCFR were 5.3% (95% CI: 3.5%, 7.5%) for Scenario 1 and 8.4% (95% CI: 5.3%, 12.3%) for Scenario 2. The basic reproduction number was estimated to be 2.1 (95% CI: 2.0, 2.2) and 3.2 (95% CI: 2.7, 3.7) for Scenarios 1 and 2, respectively. Based on these results, we argued that the current COVID-19 epidemic has a substantial potential for causing a pandemic. The proposed approach provides insights in early risk assessment using publicly available data.

scholarly journals Effect of evidence updates on key determinants of measles vaccination impact: a DynaMICE modelling study in ten high-burden countries

BMC Medicine ◽  
2021 ◽  
Vol 19 (1) ◽  
Author(s):  
Han Fu ◽  
Kaja Abbas ◽  
Petra Klepac ◽  
Kevin van Zandvoort ◽  
Hira Tanvir ◽  
...  
Keyword(s):  
Basic Reproduction Number ◽  
Vaccine Efficacy ◽  
Reproduction Number ◽  
Case Fatality ◽  
Routine Immunisation ◽  
High Burden ◽  
Fatality Risk ◽  
Measles Vaccination ◽  
Case Fatality Risk ◽  
The Basic Reproduction Number

Abstract Background Model-based estimates of measles burden and the impact of measles-containing vaccine (MCV) are crucial for global health priority setting. Recently, evidence from systematic reviews and database analyses have improved our understanding of key determinants of MCV impact. We explore how representations of these determinants affect model-based estimation of vaccination impact in ten countries with the highest measles burden. Methods Using Dynamic Measles Immunisation Calculation Engine (DynaMICE), we modelled the effect of evidence updates for five determinants of MCV impact: case-fatality risk, contact patterns, age-dependent vaccine efficacy, the delivery of supplementary immunisation activities (SIAs) to zero-dose children, and the basic reproduction number. We assessed the incremental vaccination impact of the first (MCV1) and second (MCV2) doses of routine immunisation and SIAs, using metrics of total vaccine-averted cases, deaths, and disability-adjusted life years (DALYs) over 2000–2050. We also conducted a scenario capturing the effect of COVID-19 related disruptions on measles burden and vaccination impact. Results Incorporated with the updated data sources, DynaMICE projected 253 million measles cases, 3.8 million deaths and 233 million DALYs incurred over 2000–2050 in the ten high-burden countries when MCV1, MCV2, and SIA doses were implemented. Compared to no vaccination, MCV1 contributed to 66% reduction in cumulative measles cases, while MCV2 and SIAs reduced this further to 90%. Among the updated determinants, shifting from fixed to linearly-varying vaccine efficacy by age and from static to time-varying case-fatality risks had the biggest effect on MCV impact. While varying the basic reproduction number showed a limited effect, updates on the other four determinants together resulted in an overall reduction of vaccination impact by 0.58%, 26.2%, and 26.7% for cases, deaths, and DALYs averted, respectively. COVID-19 related disruptions to measles vaccination are not likely to change the influence of these determinants on MCV impact, but may lead to a 3% increase in cases over 2000–2050. Conclusions Incorporating updated evidence particularly on vaccine efficacy and case-fatality risk reduces estimates of vaccination impact moderately, but its overall impact remains considerable. High MCV coverage through both routine immunisation and SIAs remains essential for achieving and maintaining low incidence in high measles burden settings.

scholarly journals Mathematical Perspective of Covid-19 Pandemic: Disease Extinction Criteria in Deterministic and Stochastic Models

2020 ◽  
Author(s):  
Debadatta Adak ◽  
Abhijit Majumder ◽  
Nandadulal Bairagi
Keyword(s):  
Basic Reproduction Number ◽  
Stochastic System ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Case Fatality ◽  
Deterministic System ◽  
Globally Asymptotically Stable ◽  
Epidemic Curve ◽  
Interior Equilibrium ◽  
The Basic Reproduction Number

AbstractThe world has been facing the biggest virological invasion in the form of Covid-19 pandemic since the beginning of the year 2020. In this paper, we consider a deterministic epidemic model of four compartments classified based on the health status of the populations of a given country to capture the disease progression. A stochastic extension of the deterministic model is further considered to capture the uncertainty or variation observed in the disease transmissibility. In the case of a deterministic system, the disease-free equilibrium will be globally asymptotically stable if the basic reproduction number is less than unity, otherwise, the disease persists. Using Lyapunov functional methods, we prove that the infected population of the stochastic system tends to zero exponentially almost surely if the basic reproduction number is less than unity. The stochastic system has no interior equilibrium, however, its asymptotic solution is shown to fluctuate around the endemic equilibrium of the deterministic system under some parametric restrictions, implying that the infection persists. A case study with the Covid-19 epidemic data of Spain is presented and various analytical results have been demonstrated. The epidemic curve in Spain clearly shows two waves of infection. The first wave was observed during March-April and the second wave started in the middle of July and not completed yet. A real-time basic reproduction number has been given to illustrate the epidemiological status of Spain throughout the study period. Estimated cumulative numbers of confirmed and death cases are 1,613,626 and 42,899, respectively, with case fatality rate 2.66 per cent till the deadly virus is eliminated from Spain.

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