Predicting the number of reported and unreported cases for the COVID-19 epidemics in China, South Korea, Italy, France, Germany and United Kingdom

1SummaryBackgroundThe novel coronavirus (SARS-CoV-2) is currently causing concern in the medical, epidemiological and mathematical communities as the virus is rapidly spreading around the world. Internationally, there are more than 1 200 000 cases detected and confirmed in the world on April 6. The asymptomatic and mild symptomatic cases are just going to be really crucial for us to understand what is driving this epidemic to transmit rapidly. Combining a mathematical model of severe (SARS-CoV-transmission with data from China, South Korea, Italy, France, Germany and United Kingdom, we provide the epidemic predictions of the number of reported and unreported cases for the SARS-CoV-2 epidemics and evaluate the effectiveness of control measures for each country.MethodsWe combined a mathematical model with data on cumulative confirmed cases from China, South Korea, Italy, France, Germany and United Kingdom to provide the epidemic predictions and evaluate the effectiveness of control measures. We divide infectious individuals into asymptomatic and symptomatic infectious individuals. The symptomatic infectious phase is also divided into reported (severe symptoms) and unreported (mild symptoms) cases. In fact, there exists a period for the cumulative number of reported cases to grow (approximately) exponentially in the early phase of virus transmission which is around the implementation of the national prevention and control measures. We firstly combine the date of the implementation of the measures with the daily and cumulative data of the reported confirmed cases to find the most consistent period for the cumulative number of reported cases to grow − approximately exponentially with the formula χ1 exp(χ2t) χ3, thus we can determine the parameters χ1, χ2, χ3 in this formula and then determine the parameters and initial conditions for our model by using this formula and the plausible biological parameters for SARS-CoV-2 based on current evidence.We then provide the epidemic predictions, evaluate the effectiveness of control measures by simulations of our model.FindingsBased on the simulations using multiple groups of parameters (d1, d2, N), here [d1, d2] is the consistent period for the cumulative number of reported cases to grow approximately exponentially with the formula χ1 exp(χ2t) χ3 and N is the date at which public intervention measures became effective, we found that the ranges of the turning point, the final size of reported and unreported cases are respectively Feb.6 − 7, 67 000 − 69 000 and 45 000 − 46 000 for China, Feb.29−Mar.1, 9 000 − 9 400and 2 250 − 2 350 for South Korea, Mar.24 − 26, 156 000 − 177 000, and 234 000 − 265 000 for Italy, Mar.30−Apr.9, 104 000 − 212 000, and 177 000 − 318 000 for France, Mar.30−Apr.20, 141 000 − 912 000, and 197 000 − 1 369 000 for Germany, Apr.1−May12, 140 000 − 473 000, and 210 000 − 709 000 for UnitedKingdom. Our prediction relies on the cumulative data of the reported confirmed cases. As more data become available, the ranges become smaller and smaller, that means the prediction becomes better and better. It is evident that our estimates and simulations have shown good correspondence with the distribution of the cumulative data available of the reported confirmed cases for each country and in particularly, the curves plotted by using different parameter groups (d1, d2, N) for reported and unreported cases tend to be consistent in China and South Korea (see (e) in Figures 2-3). For Italy, France, Germany and United Kingdom, the prediction can be updated to higher accuracy with on-going day by day reported case data (see Figures 4-7).InterpretationWe used the plausible biological parameters f, ν, η for SARS-CoV-2 based on current evidence which might be refined as more comprehensive data become available. Our prediction also relies on the cumulative data of the reported confirmed cases. Using multiple groups of parameters (d1, d2, N), we have attempted to make the best possible prediction using the available data. We found that with more cumulative data available, the curves plotted by using different parameter groups (d1, d2, N) for reported and unreported cases will be closer and closer, and finally tend to be consistent. This shows that when we have no enough cumulative data available, we need to use all possible parameter groups to predict the range of turning point, the final size of reported and unreported cases. When we have enough cumulative data, for example, when we get the data after the turning point, we only need to use any one of these parameter groups to get a prediction with high accuracy.FundingNSFC (Grant No. 11871007), NSFC and CNRS (Grant No. 11811530272) and the Fundamental Research Funds for the Central Universities.

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Hidden periods, duration and final size of COVID-19 pandemic

10.1101/2020.05.10.20097147 ◽

2020 ◽

Cited By ~ 1

Author(s):

Igor Nesteruk

Keyword(s):

South Korea ◽

Parameter Identification ◽

Statistical Approach ◽

Cumulative Number ◽

Final Size ◽

Current Trends ◽

The World ◽

If Current

The SIR (susceptible-infected-removed) model, statistical approach for the parameter identification and the official WHO data about the confirmed cumulative number of cases were used to estimate the characteristics of COVID-19 pandemic in USA, Germany, UK, South Korea and in the world. Epidemic in every country has rather long hidden period before fist cases were confirmed. In particular, the pandemic began in China no later than October, 2019. If current trends continue, the end of the pandemic should be expected no earlier than March 2021, the global number of cases will exceed 5 million.

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Prediction of confinement effects on the number of Covid-19 outbreak in Algeria

Mathematical Modelling of Natural Phenomena ◽

10.1051/mmnp/2020028 ◽

2020 ◽

Vol 15 ◽

pp. 37 ◽

Cited By ~ 1

Author(s):

Ali Moussaoui ◽

Pierre Auger

Keyword(s):

Reproduction Number ◽

Control Measures ◽

Cumulative Number ◽

Time Data ◽

Final Size ◽

First Case ◽

Algerian Population ◽

Fast Change ◽

Real Time Data ◽

The Basic Reproduction Number

The first case of coronavirus disease 2019 (COVID-19) in Algeria was reported on 25 February 2020. Since then, it has progressed rapidly and the number of cases grow exponentially each day. In this article, we utilize SEIR modelling to forecast COVID-19 outbreak in Algeria under two scenarios by using the real-time data from March 01 to April 10, 2020. In the first scenario: no control measures are put into place, we estimate that the basic reproduction number for the epidemic in Algeria is 2.1, the number of new cases in Algeria will peak from around late May to early June and up to 82% of the Algerian population will likely contract the coronavirus. In the second scenario, at a certain date T, drastic control measures are taken, people are being advised to self-isolate or to quarantine and will be able to leave their homes only if necessary. We use SEIR model with fast change between fully protected and risky states. We prove that the final size of the epidemic depends strongly on the cumulative number of cases at the date when we implement intervention and on the fraction of the population in confinement. Our analysis shows that the longer we wait, the worse the situation will be and this very quickly produces.

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A reductive analysis of a compartmental model for COVID-19: data assimilation and forecasting for the United Kingdom

10.1101/2020.05.27.20114868 ◽

2020 ◽

Author(s):

G. Ananthakrishna ◽

Jagadish Kumar

Keyword(s):

United Kingdom ◽

Turning Point ◽

Total Population ◽

Deterministic Model ◽

Logistic Equation ◽

Original Model ◽

Cumulative Number ◽

Full Model ◽

The United Kingdom ◽

Model Equations

We introduce a deterministic model that partitions the total population into the susceptible, infected, quarantined, and those traced after exposure, the recovered and the deceased. We hypothesize ‘accessible population for transmission of the disease’ to be a small fraction of the total population, for instance when interventions are in force. This hypothesis, together with the structure of the set of coupled nonlinear ordinary differential equations for the populations, allows us to decouple the equations into just two equations. This further reduces to a logistic type of equation for the total infected population. The equation can be solved analytically and therefore allows for a clear interpretation of the growth and inhibiting factors in terms of the parameters in the full model. The validity of the ‘accessible population’ hypothesis and the efficacy of the reduced logistic model is demonstrated by the ease of fitting the United Kingdom data for the cumulative infected and daily new infected cases. The model can also be used to forecast further progression of the disease. In an effort to find optimized parameter values compatible with the United Kingdom coronavirus data, we first determine the relative importance of the various transition rates participating in the original model. Using this we show that the original model equations provide a very good fit with the United Kingdom data for the cumulative number of infections and the daily new cases. The fact that the model calculated daily new cases exhibits a turning point, suggests the beginning of a slow-down in the spread of infections. However, since the rate of slowing down beyond the turning point is small, the cumulative number of infections is likely to saturate to about 3.52 × 105 around late July, provided the lock-down conditions continue to prevail. Noting that the fit obtained from the reduced logistic equation is comparable to that with the full model equations, the underlying causes for the limited forecasting ability of the reduced logistic equation are elucidated. The model and the procedure adopted here are expected to be useful in fitting the data for other countries and in forecasting the progression of the disease.

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Generalized logistic growth modeling of the COVID-19 outbreak in 29 provinces in China and in the rest of the world

10.1101/2020.03.11.20034363 ◽

2020 ◽

Cited By ~ 23

Author(s):

Ke Wu ◽

Didier Darcet ◽

Qian Wang ◽

Didier Sornette

Keyword(s):

South Korea ◽

Growth Model ◽

Significant Risk ◽

Control Measures ◽

Upper And Lower Bounds ◽

Logistic Growth ◽

Italian Population ◽

The World ◽

Logistic Growth Model ◽

The Impact

AbstractBackgroundthe COVID-19 has been successfully contained in China but is spreading all over the world. We use phenomenological models to dissect the development of the epidemics in China and the impact of the drastic control measures both at the aggregate level and within each province. We use the experience from China to analyze the calibration results on Japan, South Korea, Iran, Italy and Europe, and make future scenario projections.Methodswe calibrate the logistic growth model, the generalized logistic growth model, the generalized growth model and the generalized Richards model to the reported number of infected cases from Jan. 19 to March 10 for the whole of China, 29 provinces in China, four severely affected countries and Europe as a whole. The different models provide upper and lower bounds of our scenario predictions.ResultsWe quantitatively document four phases of the outbreak in China with a detailed analysis on the heterogenous situations across provinces. Based on Chinese experience, we identify a high risk in Japan with estimated total confirmed cases as of March 25 being 1574 (95% CI: [880, 2372]), and 5669 (95% CI: [988, 11340]) by June. For South Korea, we expect the number of infected cases to approach the ceiling, 7928 (95% CI: [6341, 9754]), in 20 days. We estimate 0.15% (95% CI: [0.03%, 0.30%]) of Italian population to be infected in a positive scenario. We would expect 114867 people infected in Europe in 10 days, in a negative but probable scenario, corresponding to 0.015% European population.ConclusionsThe extreme containment measures implemented by China were very effective with some instructive variations across provinces. For other countries, it is almost inevitable to see the continuation of the outbreak in the coming months. Japan and Italy are in serious situations with no short-term end to the outbreak to be expected. There is a significant risk concerning the upcoming July 2020 Summer Olympics in Tokyo. Iran’s situation is highly uncertain with unclear and negative future scenarios, while South Korea is approaching the end of the outbreak. Both Europe and the USA are at early stages of the outbreak, posing significant health and economic risks to the world in absence of serious measures.

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The Copenhagen Chiasm

The Unconstructable Earth ◽

10.5422/fordham/9780823282586.003.0100 ◽

2018 ◽

pp. 25-26

Author(s):

Frédéric Neyrat

Keyword(s):

Climate Change ◽

United Kingdom ◽

Executive Director ◽

Turning Point ◽

Crime Scene ◽

The United Kingdom ◽

The World ◽

History Of ◽

The City

“This evening, the city of Copenhagen is a crime scene, with those responsible fleeing for the airport.” It was in this manner that John Sauven, the executive director of Greenpeace for the United Kingdom, expressed himself following the Copenhagen summit on climate change.1 A crime? What sort of crime? What exactly happened during this summit? More than likely, no kind of event that would be capable of immediately changing the history of the world. But nevertheless, there was a noticeable turning point in relation to how societies were discussing the management of climate change; there was a revelatory moment in regard to what we have taken to calling the ...

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Policy and Law Assessment of COVID-19 Based on Smooth Transition Autoregressive Model

Complexity ◽

10.1155/2021/6659117 ◽

2021 ◽

Vol 2021 ◽

pp. 1-13

Author(s):

Jieqi Lei ◽

Xuyuan Wang ◽

Yiming Zhang ◽

Lian Zhu ◽

Lin Zhang

Keyword(s):

Prevention And Control ◽

Control Measures ◽

Smooth Transition ◽

Cumulative Number ◽

Star Model ◽

The World ◽

Transition Points ◽

And Control ◽

The Impact ◽

Smooth Transition Autoregressive

As of the end of October 2020, the cumulative number of confirmed cases of COVID-19 has exceeded 45 million and the cumulative number of deaths has exceeded 1.1 million all over the world. Faced with the fatal pandemic, countries around the world have taken various prevention and control measures. One of the important issues in epidemic prevention and control is the assessment of the prevention and control effectiveness. Changes in the time series of daily new confirmed cases can reflect the impact of policies in certain regions. In this paper, a smooth transition autoregressive (STAR) model is applied to investigate the intrinsic changes during the epidemic in certain countries and regions. In order to quantitatively evaluate the influence of the epidemic control measures, the sequence is fitted to the STAR model; then, comparisons between the dates of transition points and those of releasing certain policies are applied. Our model well fits the data. Moreover, the nonlinear smooth function within the STAR model reveals that the implementation of prevention and control policies is effective in some regions with different speeds. However, the ineffectiveness is also revealed and the threat of a second wave had already emerged.

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Temperature Significantly Change COVID-19 Transmission in 429 cities

10.1101/2020.02.22.20025791 ◽

2020 ◽

Cited By ~ 69

Author(s):

Mao Wang ◽

Aili Jiang ◽

Lijuan Gong ◽

Lina Lu ◽

Wenbin Guo ◽

...

Keyword(s):

Minimum Temperature ◽

Factor Model ◽

Control Measures ◽

Maximum Temperature ◽

Cumulative Number ◽

The World ◽

Temperature Group ◽

Linear Mixture Model ◽

Maximum Temperatures ◽

Lower Temperature

AbstractBackgroundThere is no evidence supporting that temperature changes COVID-19 transmission.MethodsWe collected the cumulative number of confirmed cases of all cities and regions affected by COVID-19 in the world from January 20 to February 4, 2020, and calculated the daily means of the average, minimum and maximum temperatures in January. Then, restricted cubic spline function and generalized linear mixture model were used to analyze the relationships.ResultsThere were in total 24,139 confirmed cases in China and 26 overseas countries. In total, 16,480 cases (68.01%) were from Hubei Province. The lgN rose as the average temperature went up to a peak of 8.72°C and then slowly declined. The apexes of the minimum temperature and the maximum temperature were 6.70°C and 12.42°C respectively. The curves shared similar shapes. Under the circumstance of lower temperature, every 1°C increase in average, minimum and maximum temperatures led to an increase of the cumulative number of cases by 0.83, 0.82 and 0.83 respectively. In the single-factor model of the higher-temperature group, every 1°C increase in the minimum temperature led to a decrease of the cumulative number of cases by 0.86.ConclusionThe study found that, to certain extent, temperature could significant change COVID-19 transmission, and there might be a best temperature for the viral transmission, which may partly explain why it first broke out in Wuhan. It is suggested that countries and regions with a lower temperature in the world adopt the strictest control measures to prevent future reversal.

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Comparative analysis of the first wave of the COVID-19 pandemic in South Korea, Italy, Spain, France, Germany, the United Kingdom, the USA and the New-York state

10.1101/2020.11.20.20235689 ◽

2020 ◽

Author(s):

Luis Alvarez

Keyword(s):

New York ◽

United Kingdom ◽

South Korea ◽

Exponential Growth ◽

New York State ◽

Cumulative Number ◽

York State ◽

The United Kingdom ◽

The Usa ◽

The Impact

AbstractWe use an exponential growth model to analyze the first wave of the COVID-19 pandemic in South Korea, Italy, Spain, France, Germany, the United Kingdom, the USA and the New-York state. This model uses the number of officially reported patients tested positive and deaths to estimate an infected hindcast of the cumulative number of patients who later tested positive or who later die. For each region, an epidemic timeline is established, obtaining a precise knowledge of the chronology of the main epidemiological events during the full course of the first wave. It includes, in particular, the time that the virus has been in free circulation before the impact of the social distancing measures were observable. The results of the study suggest that among the analyzed regions, only South Korea and Germany possessed, at the beginning of the epidemic, a testing capacity that allowed to correctly follow the evolution of the epidemic. Anticipation in taking measures in these two countries caused the virus to spend less time in free circulation than in the rest of the regions. The analysis of the growth rates in the different regions suggests that the exponential growth rate of the cumulative number of infected, when the virus is in free circulation, is around 0.250737. In addition, we also study the ability of the model to properly forecast the epidemic spread at the beginning of the epidemic outbreak when very little data and information about the coronavirus were available. In the case of France, we obtain a reasonable estimate of the peak of the new cases of patients tested positive 9 days in advance and only 7 days after the implementation of a strict lockdown.

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Estimation of the final size of the second phase of the coronavirus COVID 19 epidemic by the logistic model

10.1101/2020.03.11.20024901 ◽

2020 ◽

Cited By ~ 20

Author(s):

Milan Batista

Keyword(s):

South Korea ◽

Regression Model ◽

Logistic Model ◽

Logistic Growth ◽

Second Phase ◽

Peak Time ◽

Final Size ◽

The World ◽

Growth Regression

AbstractIn the note, the logistic growth regression model is used for the estimation of the final size and its peak time of the coronavirus epidemic in China, South Korea, and the rest of the World.

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Tracking the onset date of the community spread of SARS-CoV-2 in Western Countries

10.1101/2020.04.20.20073007 ◽

2020 ◽

Cited By ~ 2

Author(s):

Edson Delatorre ◽

Daiana Mir ◽

Tiago Gräf ◽

Gonzalo Bello

Keyword(s):

Western Europe ◽

Early Stage ◽

Control Measures ◽

Onset Date ◽

Cumulative Number ◽

Western Countries ◽

The World ◽

Community Transmission ◽

And Control ◽

Precise Time

ABSTRACTThe SARS-CoV-2 rapidly spread around the world during 2020, but the precise time in which the virus began to spread locally is currently unknown for most countries. Here, we estimate the probable onset date of the community spread of SARS-CoV-2 from the cumulative number of deaths reported during the early stage of the epidemic in Western Europe and the Americas. Our results support that SARS-CoV-2 probably started to spread locally in all western countries analyzed between the middle of January and early February 2020, thus long before community transmission was officially recognized and control measures were implemented.

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