Forecasting the changes between endemic and epidemic phases of a contagious disease, with the example of COVID-19 (preprint)

Predicting the endemic/epidemic transition during the temporal evolution of a contagious disease. Methods: Defining indicators for detecting the transition endemic/epidemic, with four scalars to be compared, calculated from the daily reported news cases: coefficient of variation, skewness, kurtosis, and entropy. The indicators selected are related to the shape of the empirical distribution of the new cases observed over 14 days. This duration has been chosen to smooth out the effect of weekends when fewer new cases are registered. For finding a forecasting variable, we have used the PCA (principal component analysis), whose first principal component (a linear combination of the selected indicators) explains a large part of the observed variance and can then be used as a predictor of the phenomenon studied (here the occurrence of an epidemic wave). Results: A score has been built from the four proposed indicators using a Principal Component Analysis (PCA), which allows an acceptable level of forecasting performance by giving a realistic retro-predicted date for the rupture of the stationary endemic model corresponding to the entrance in the epidemic exponential growth phase. This score is applied to the retro-prediction of the limits of the different phases of the COVID-19 outbreak in successive endemic/epidemic transitions and three countries, France, India, and Japan. Conclusion: We provided a new forecasting method for predicting an epidemic wave occurring after an endemic phase for a contagious disease.

Vaccine efficacy for COVID-19 outbreak in New York City (preprint)

This article aims to study the COVID-19 data for New York City. We use both the daily number of second does vaccination and the daily number of reported cases for New York City. This article provides a method to combine an epidemic model and such data. We explore the influence of vaccine efficacy on our results.

What can we learn from COVID-19 data by using epidemic models with unidentified infectious cases? (preprint)

Background: The COVID-19 epidemic, which started in late December 2019 and rapidly spread throughout the world, was accompanied by an unprecedented release of reported case data. Our objective is to propose a fresh look at this data by coupling a phenomenological description to the epidemiological dynamics. Methods: We use a phenomenological model to describe and regularize the data. This model can be matched by a single mathematical model reproducing the epidemiological dynamics with a time-dependent transmission rate. We provide a method to compute this transmission rate and reconstruct the changes in the social interactions between people as well as changes in host-pathogen interactions. This method is applied to the cumulative case data of 8 different geographic areas. Findings: We reconstruct the transmission rate from the data, therefore we are in position to understand the contribution of the dynamical effects of social interactions (contacts between individuals) and the contribution of the dynamics of the epidemic. We deduce from the comparison of several instantaneous reproduction numbers that the social effects are the most important in the dynamic of COVID-19. We obtain an instantaneous reproduction number that stays below $3.5$ from early beginning of the epidemic. Conclusion: The instantaneous reproduction number staying below $3.5$ implies that it is sufficient to vaccinate $71\%$ of the population in each state or country considered in our study. Therefore assuming the vaccines will remain efficient against the new variants, and to be more confident it is sufficient to vaccinate $75-80\%$ to get rid of COVID-19 in each state or country. Funding: This research was funded by the Agence Nationale de la Recherche in France (Project name: MPCUII (PM) and (QG))

Clarifying Predictions for COVID-19 from Testing Data: The Example of New York State (preprint)

With the spread of COVID-19 across the world, a large amount of data on reported cases has become available. We are studying here a potential bias induced by the daily number of tests which may be insufficient or vary over time. Indeed, tests are hard to produce at the early stage of the epidemic and can therefore be a limiting factor in the detection of cases. Such a limitation may have a strong impact on the reported cases data. Indeed, some cases may be missing from the official count because the number of tests was not sufficient on a given day. In this work, we propose a new differential equation epidemic model which uses the daily number of tests as an input. We obtain a good agreement between the model simulations and the reported cases data coming from the state of New York. We also explore the relationship between the dynamic of the number of tests and the dynamics of the cases. We obtain a good match between the data and the outcome of the model. Finally, by multiplying the number of tests by 2, 5, 10, and 100 we explore the consequences for the number of reported cases.

SI Epidemic Model Applied to COVID-19 Data in Mainland China (preprint)

The article is devoted to the parameters identification in the SI model. We consider several methods, starting with an exponential fit of the early cumulative data of SARS-CoV2 in mainland China. The present methodology provides a way to compute the parameters at the early stage of the epidemic. Next, we establish an identifiability result. Then we use the Bernoulli-Verhulst model as a phenomenological model to fit the data and derive some results on the parameters identification. The last part of the paper is devoted to some numerical algorithms to fit a daily piecewise constant rate of transmission.

SI epidemic model applied to COVID-19 data in mainland China (preprint)

The article is devoted to the parameters identification in the SI model. We consider several methods, starting with an exponential fit of the early cumulative data of Sars-CoV2 in mainland China. The present methodology provides a way to compute the parameters at the early stage of the epidemic. Next, we establish an identifiability result. Then we use the Bernoulli-Verhulst model as a phenomenological model to fit the data and derive some results on the parameters identification. The last part of the paper is devoted to some numerical algorithms to fit a daily piecewise constant rate of transmission.

Clarifying predictions for COVID-19 from testing data: the example of New-York State (preprint)

In this article, we use testing data as an input of a new epidemic model. We get nice a concordance between the best fit the model to the reported cases data for New-York state. We also get a good concordance of the testing dynamic and the epidemics dynamic in the cumulative cases. Finally, we can investigate the effect of multiplying the number of tests by 2, 5, 10, and 100 to investigate the consequences on the reduction of the number of reported cases.

Unreported Cases for Age Dependent COVID-19 Outbreak in Japan (preprint)

We investigate the age structured data for the COVID-19 outbreak in Japan. We consider epidemic mathematical model with unreported infectious patient with and without age structure. In particular, we build a new mathematical model which allows to take into account differences in the response of patients to the disease according to their age. This model also allows for a heterogeneous response of the population to the social distancing measures taken by the local government. We fit this model to the observed data and obtain a snapshot of the effective transmissions occurring inside the population at different times, which indicates where and among whom the disease propagates after the start of the public measures.

Global Analysis of SARS-COV-2 Mitigation Impact Reveals an Arabian Peninsula Cluster with High Infection Rates and Shared Indicators (preprint)

Background SARS-CoV-2 is a novel virus that appeared in China in November 2019 and spread rapidly. With no vaccine or effective treatment, countries have adopted different mitigation measures to reduce SARS-COV-2 spread with different efficacy.MethodsWe mapped the impact of mitigation measures across different countries. We compared regional SARS-COV-2 population burden via Kruskal-Wallis statistical testing. We analyzed time of adoption of mitigation measures and the impact of PCR testing on mitigation impact. We analyzed the association of climate, health, demographic and economic indicators with mitigation impact via non-parametric correlation tests. We performed mechanistic modelling of to predict short-term SARS-COV-2 case numbers in selected countries. ResultsMany countries showed a reduction of infection rates within one month of implementing mitigation measures. However, we identified a geographic cluster of countries centered on the Arabian Peninsula (AP) that show a high SARS-COV-2 population burden despite early adoption of mitigation measures. We find that higher air pollution levels (p=0.01), higher CO2 emissions (p=0.03) and younger population (p=0.02) were associated with reduced mitigation impact in AP countries. We also show that mechanistic modelling can closely predict confirmed case numbers in the short term.ConclusionsThe impact of mitigation measures varies greatly between countries. Countries with similar profiles as AP countries should adopt more stringent mitigation measures to more rapidly reduce SARS-CoV-2 spread. Specific interventions targeting young people may also be effective in reducing SARS-COV-2 spread.

Unreported cases for Age Dependent COVID-19 Outbreak in Japan (preprint)

We investigate the age structured data for the COVID-19 outbreak in Japan. We consider epidemic mathematical model with unreported infectious patient with and without age structure. In particular, we build a new mathematical model which allows to take into account differences in the response of patients to the disease according to their age. This model also allows for a heterogeneous response of the population to the social distancing measures taken by the local government. We fit this model to the observed data and obtain a snapshot of the effective transmissions occurring inside the population at different times, which indicates where and among whom the disease propagates after the start of the public measures.

Estimating the last day for COVID-19 outbreak in mainland China (preprint)

Our main aim is to estimate the end of the first wave epidemic of COVID-19 outbreak in mainland China. We developed mathematical models to predict reasonable bounds on the date of end of the COVID-19 epidemics in mainland China with strong quarantine and testing measures for a sufficiently long time. We used reported data in China from January 20, 2020 to April 9, 2020. We firstly used a deterministic approach to obtain a formula to compute the probability distribution of the extinction date by combining the models and continuous-time Markov processes. Then we present the individual based model (IMB) simulations to compare the result by deterministic approach and show the absolute difference between the estimated cumulative probability distribution computed by simulations and formula. We provide the predictions of the end of the first wave epidemic for different fractions $f$ of asymptomatic infectious that become reported symptomatic infectious.

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

We model the COVID-19 coronavirus epidemics in China, South Korea, Italy, France, Germany and United Kingdom. We use early reported case data to predict the cumulative number of reported cases to a final size in each country. The key features of our model are the timing of implementation of major public policies restricting social movement, the identification and isolation of unreported cases, and the impact of asymptomatic infectious cases.

A model to predict COVID-19 epidemics withapplications to South Korea, Italy, and Spain (preprint)

In this work, our team develops a differential equations model of COVID-19 epidemics. Our goal is to predict forward in time the future number of cases from early reported case data in regions throughout the world. Our model incorporates the following important elements of COVID-19 epidemics: (1) the number of asymptomatic infectious individuals (with very mild or no symptoms), (2) the number of symptomatic reported infectious individuals (with severe symptoms) and (3) the number of symptomatic unreported infectious individuals (with less severe symptoms). We apply our model to COVID-!9 epidemics in South Korea, Italy and Spain.

Modelling the COVID-19 epidemics in Brasil: Parametric identification and public health measures influence (preprint)

A SIRU-type epidemic model is employed for the prediction of the COVID-19 epidemy evolution in Brazil, and analyse the influence of public health measures on simulating the control of this infectious disease. Since the reported cases are typically only a fraction of the total number of the symptomatic infectious individuals, the model accounts for both reported and unreported cases. Also, the model allows for a time variable functional form of both the transmission rate and the fraction of asymptomatic infectious that become reported symptomatic individuals, so as to reflect public health interventions, towards its control, along the course of the epidemic evolution. An analytical exponential behaviour for the accumulated reported cases evolution is assumed at the onset of the epidemy, for explicitly estimating initial conditions, while a Bayesian inference approach is adopted for parametric estimations employing the present direct problem model with the data from the known portion of the epidemics evolution, represented by the time series for the reported cases of infected individuals. The direct-inverse problem analysis is then employed with the actual data from China, with the initial phase of the data been employed for the parametric estimation and the remaining data being used for validation of the predictive capability of the proposed approach. The full dataset for China is then employed in another parameter identification, aimed at refining the values for the average times that asymptomatic infectious individuals and that symptomatic individuals remain infectious. Following this validation, the available data on reported cases in Brazil from February 15th till March 29th, 2020, is used for estimating parameters and then predict the epidemy evolution from these initial conditions. As for the China analysis, the data for the reported cases in Brazil from March 30th till April 23rd are reserved for validation of the model. Finally, public health interventions are simulated, aimed at evaluating the effects on the disease spreading, by acting on both the transmission rate and the fraction of the total number of the symptomatic infectious individuals, considering time variable exponential behaviours for these two parameters, usually assumed constant in epidemic evolutions without intervention. It is demonstrated that a combination of actions to affect both parameters can have a more effective result in the control of the epidemy dynamics.

Predicting the number of reported and unreported cases for the COVID-19 epidemic in South Korea, Italy, France and Germany (preprint)

We model the COVID-19 coronavirus epidemic in South Korea, Italy, France, and Germany. We use early reported case data to predict the cumulative number of reported cases to a final size. The key features of our model are the timing of implementation of major public policies restricting social movement, the identification and isolation of unreported cases, and the impact of asymptomatic infectious cases.

Predicting the cumulative number of cases for the COVID-19 epidemic in China from early data (preprint)

We model the COVID-19 coronavirus epidemic in China. We use early reported case data to predict the cumulative number of reported cases to a final size. The key features of our model are the timing of implementation of major public policies restricting social movement, the identification and isolation of unreported cases, and the impact of asymptomatic infectious cases.