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

Modeling vaccination prioritization strategies for post-pandemic COVID-19 in the Republic of Korea accounting for under-reporting and age-structure

BACKGROUND

Vaccination has played a key role in limiting the impacts of COVID-19. Even though the acute phase of the COVID-19 pandemic is now over, the potential for substantial numbers of cases and deaths due to novel SARS-CoV-2 variants remains. In the Republic of Korea, a strategy of vaccinating individuals in high-risk groups annually began in October 2023.

METHODS

We used mathematical modeling to assess the effectiveness of alternative vaccination strategies under different assumptions about the number of available vaccine doses. An age-structured transmission model was developed using vaccination and seropositivity data. Various vaccination scenarios were considered, taking into account the effect of undetected or unreported cases (with different levels of reporting by age group): S1: prioritizing vaccination towards the oldest individuals; S2: prioritizing vaccination towards the youngest individuals; and S3: spreading vaccines among all age groups.

RESULTS

Our analysis reveals three key findings. First, administering vaccines to older age groups reduces the number of deaths, while instead targeting younger individuals reduces the number of infections. Second, with approximately 6,000,000 doses available annually, it is recommended that older age groups are prioritized for vaccination, achieving a substantial reduction in the number of deaths compared to a scenario without vaccination. Finally, since case detection (and subsequent isolation) affects transmission, the number of cumulative cases was found to be affected substantially by changes in the reporting rate.

CONCLUSIONS

In conclusion, vaccination and case detection (facilitated by contact tracing) both play important roles in limiting the impacts of COVID-19. The mathematical modeling approach presented here provides a framework for assessing the effectiveness of different vaccination strategies in scenarios with limited vaccine supply.

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

BACKGROUND

Predicting the endemic/epidemic transition during the temporal evolution of a contagious disease.

METHODS

Indicators for detecting the transition endemic/epidemic, with four scalars to be compared, are 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 principal component analysis (PCA), 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 the 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 for 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.

A six-compartment model for COVID-19 with transmission dynamics and public health strategies

The global crisis of the COVID-19 pandemic has highlighted the need for mathematical models to inform public health strategies. The present study introduces a novel six-compartment epidemiological model that uniquely incorporates a higher isolation rate for unreported symptomatic cases of COVID-19 compared to reported cases, aiming to enhance prediction accuracy and address the challenge of initial underreporting. Additionally, we employ optimal control theory to assess the cost-effectiveness of interventions and adapt these strategies to specific epidemiological scenarios, such as varying transmission rates and the presence of asymptomatic carriers. By applying this model to COVID-19 data from India (30 January 2020 to 24 November 2020), chosen to capture the initial outbreak and subsequent waves, we calculate a basic reproduction number of 2.147, indicating the high transmissibility of the virus during this period in India. A sensitivity analysis reveals the critical impact of detection rates and isolation measures on disease progression, showing the robustness of our model in estimating the basic reproduction number. Through optimal control simulations, we demonstrate that increasing isolation rates for unreported cases and enhancing detection reduces the spread of COVID-19. Furthermore, our cost-effectiveness analysis establishes that a combined strategy of isolation and treatment is both more effective and economically viable. This research offers novel insights into the efficacy of non-pharmaceutical interventions, providing a tool for strategizing public health interventions and advancing our understanding of infectious disease dynamics.

Data-driven mathematical modeling approaches for COVID-19: A survey

In this review, we successively present the methods for phenomenological modeling of the evolution of reported and unreported cases of COVID-19, both in the exponential phase of growth and then in a complete epidemic wave. After the case of an isolated wave, we present the modeling of several successive waves separated by endemic stationary periods. Then, we treat the case of multi-compartmental models without or with age structure. Eventually, we review the literature, based on 260 articles selected in 11 sections, ranging from the medical survey of hospital cases to forecasting the dynamics of new cases in the general population. This review favors the phenomenological approach over the mechanistic approach in the choice of references and provides simulations of the evolution of the number of observed cases of COVID-19 for 10 states (California, China, France, India, Israel, Japan, New York, Peru, Spain and United Kingdom).

Forecasting the Endemic/Epidemic Transition in COVID-19 in Some Countries: Influence of the Vaccination

OBJECTIVE

The objective of this article is to develop a robust method for forecasting the transition from endemic to epidemic phases in contagious diseases using COVID-19 as a case study.

METHODS

Seven indicators are proposed for detecting the endemic/epidemic transition: variation coefficient, entropy, dominant/subdominant spectral ratio, skewness, kurtosis, dispersion index and normality index. Then, principal component analysis (PCA) offers a score built from the seven proposed indicators as the first PCA component, and its forecasting performance is estimated from its ability to predict the entrance in the epidemic exponential growth phase.

RESULTS

This score is applied to the retro-prediction of endemic/epidemic transitions of COVID-19 outbreak in seven various countries for which the first PCA component has a good predicting power.

CONCLUSION

This research offers a valuable tool for early epidemic detection, aiding in effective public health responses.

Factors associated with an increased risk of SARS-CoV-2 infection in healthcare workers in aerosol-generating disciplines

BACKGROUND

Healthcare workers (HCWs) are at a high risk of SARS-CoV-2 infection due to exposure to potentially infectious material, especially during aerosol-generating procedures (AGP). We aimed to investigate risk factors for SARS-CoV-2 infection among HCWs in medical disciplines with AGP.

METHODS

A nationwide questionnaire-based study in private practices and hospital settings was conducted between 12/16/2020 and 01/24/2021. Data on SARS-CoV-2 infections among HCWs and potential risk factors of infection were investigated.

RESULTS

2070 healthcare facilities with 25113 employees were included in the study. The overall infection rate among HCWs was 4.7%. Multivariate analysis showed that regions with higher incidence rates had a significantly increased risk of infection. Furthermore, hospital setting and HCWs in gastrointestinal endoscopy (GIE) had more than double the risk of infection (OR 2.63; 95% CI 2.50-2.82, p<0.01 and OR 2.35; 95% CI 2.25-2.50, p<0.01). For medical facilities who treated confirmed SARS-CoV-2 cases, there was a tendency towards higher risk of infection (OR 1.39; 95% CI 1.11-1.63, p=0.068).

CONCLUSION

Both factors within and outside medical facilities appear to be associated with an increased risk of infection among HCWs. Therefore, GIE and healthcare delivery setting were related to increased infection rates. Regions with higher SARS-CoV-2 incidence rates were also significantly associated with increased risk of infection.

Using real-time ascertainment rate estimate from infection and hospitalization dataset for modeling the spread of infectious disease: COVID-19 case study in the Czech Republic

We present a novel approach to estimate the time-varying ascertainment rate in almost real-time, based on the surveillance of positively tested infectious and hospital admission data. We also address the age dependence of the estimate. The ascertainment rate estimation is based on the Bayes theorem. It can be easily calculated and used (i) as part of a mechanistic model of the disease spread or (ii) to estimate the unreported infections or changes in their proportion in almost real-time as one of the early-warning signals in case of undetected outbreak emergence. The paper also contains a case study of the COVID-19 epidemic in the Czech Republic. The case study demonstrates the usage of the ascertainment rate estimate in retrospective analysis, epidemic monitoring, explanations of differences between waves, usage in the national Anti-epidemic system, and monitoring of the effectiveness of non-pharmaceutical interventions on Czech nationwide surveillance datasets. The Czech data reveal that the probability of hospitalization due to SARS-CoV-2 infection for the senior population was 12 times higher than for the non-senior population in the monitored period from the beginning of March 2020 to the end of May 2021. In a mechanistic model of COVID-19 spread in the Czech Republic, the ascertainment rate enables us to explain the links between all basic compartments, including new cases, hospitalizations, and deaths.

Final Size for Epidemic Models with Asymptomatic Transmission

The final infection size is defined as the total number of individuals that become infected throughout an epidemic. Despite its importance for predicting the fraction of the population that will end infected, it does not capture which part of the infected population will present symptoms. Knowing this information is relevant because it is related to the severity of the epidemics. The objective of this work is to give a formula for the total number of symptomatic cases throughout an epidemic. Specifically, we focus on different types of structured SIR epidemic models (in which infected individuals can possibly become symptomatic before recovering), and we compute the accumulated number of symptomatic cases when time goes to infinity using a probabilistic approach. The methodology behind the strategy we follow is relatively independent of the details of the model.

Sources, diffusion and prediction in COVID-19 pandemic: lessons learned to face next health emergency

Scholars and experts argue that future pandemics and/or epidemics are inevitable events, and the problem is not whether they will occur, but when a new health emergency will emerge. In this uncertain scenario, one of the most important questions is an accurate prevention, preparedness and prediction for the next pandemic. The main goal of this study is twofold: first, the clarification of sources and factors that may trigger pandemic threats; second, the examination of prediction models of on-going pandemics, showing pros and cons. Results, based on in-depth systematic review, show the vital role of environmental factors in the spread of Coronavirus Disease 2019 (COVID-19), and many limitations of the epidemiologic models of prediction because of the complex interactions between the new viral agent SARS-CoV-2, environment and society that have generated variants and sub-variants with rapid transmission. The insights here are, whenever possible, to clarify these aspects associated with public health in order to provide lessons learned of health policy that may reduce risks of emergence and diffusion of new pandemics having negative societal impact.

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.

Mitigating the outbreak of an infectious disease over its life cycle: A diffusion-based approach

We first qualitatively divide the cycle of an infectious disease outbreak into five distinct stages by following the adoption categorization from the diffusion theory. Next, we apply a standard mechanistic model, the susceptible-infected-recovered model, to simulate a variety of transmission scenarios and to quantify the benefits of various countermeasures. In particular, we apply the specific values of the newly infected to quantitatively divide an outbreak cycle into stages. We therefore reveal diverging patterns of countermeasures in different stages. The stage is critical in determining the evolutionary characteristics of the diffusion process. Our results show that it is necessary to employ appropriate diverse strategies in different stages over the life cycle of an infectious disease outbreak. In the early stages, we need to focus on prevention, early detection, and strict countermeasure (e.g., isolation and lockdown) for controlling an epidemic. It is better safe (i.e., stricter countermeasures) than sorry (i.e., let the virus spread out). There are two reasons why we should implement responsive and strict countermeasures in the early stages. The countermeasures are very effective, and the earlier the more total infected reduction over the whole cycle. The economic and societal burden for implementing countermeasures is relatively small due to limited affected areas, and the earlier the less burden. Both reasons change to the opposite in the late stages. The strategic focuses in the late stages become more delicate and balanced for two reasons: the same countermeasures become much less effective, and the society bears a much heavier burden. Strict countermeasures may become unnecessary, and we need to think about how to live with the infectious disease.

Population flow based spatial-temporal eigenvector filtering modeling for exploring effects of health risk factors on COVID-19

The COVID-19 pandemic has had great impact on human health and social economy. Several studies examined spatial and temporal patterns of health risk factors associated with COVID-19, but population flow spillover effect has not been sufficiently considered. In this paper, a population flow-based spatial-temporal eigenvector filtering model (FLOW-ESTF) was developed to consider spatial-temporal patterns and population flow connectivity simultaneously. The proposed FLOW-ESTF method efficiently improved model prediction accuracy, which could help the government aware of the infection risk level and to make suitable control policies. The selected population flow spatial-temporal eigenvector contributed most to modeling and the visualization of corresponding eigenvector set helped to explore the underlying spatial-temporal patterns and pandemic transmission nodes. The model coefficients could reflect how health risk factors contribute the modeling of state-level COVID-19 weekly increased cases and how their influence changed through time, which could help people and government to better aware the potential health risks and to adjust control measures at different stage. The extracted population flow spatial-temporal eigenvector not only represents influence of population flow and its spillover effects but also represents some possible omitted health risk factors. This could provide an efficient path to solve the problem of spatial and temporal autocorrelation in COVID-19 modeling and an intuitive way to discover underlying spatial patterns, which will partially compensate for the problems of insufficient consideration of potential risk variables and missing data.

Shedding light on dark figures: Steps towards a methodology for estimating actual numbers of COVID-19 infections in Germany based on Google Trends

In order to shed light on unmeasurable real-world phenomena, we investigate exemplarily the actual number of COVID-19 infections in Germany based on big data. The true occurrence of infections is not visible, since not every infected person is tested. This paper demonstrates that coronavirus-related search queries issued on Google can depict true infection levels appropriately. We find significant correlation between search volume and national as well as federal COVID-19 cases as reported by RKI. Additionally, we discover indications that the queries are indeed causal for infection levels. Finally, this approach can replicate varying dark figures throughout different periods of the pandemic and enables early insights into the true spread of future virus outbreaks. This is of high relevance for society in order to assess and understand the current situation during virus outbreaks and for decision-makers to take adequate and justifiable health measures.

COVID-19 Vaccination is not a Sufficient Public Policy to face Crisis Management of next Pandemic Threats

This study reveals that a vast vaccination campaign is a necessary but not sufficient public policy to reduce the negative impact of Coronavirus Disease 2019 (COVID-19) pandemic crisis because manifold factors guide the spread of this new infectious disease and related mortality in society. Statistical evidence here, based on a worldwide sample of countries, shows a positive correlation between people fully vaccinated and COVID-19 mortality (r = + 0.65, p-value < 0.01). Multivariate regression, controlling income per capita, confirms this finding. Results suggest that the increasing share of people vaccinated against COVID-19 seems to be a necessary but not sufficient health policy to reduce mortality of COVID-19. The findings here can be explained with the role of Peltzman effect, new variants, environmental and socioeconomic factors that affect the diffusion and negative impact of COVID-19 pandemic in society. This study extends the knowledge in this research field to design effective public policies of crisis management for facing next pandemic threats.

Adaptive SIR model with vaccination: simultaneous identification of rates and functions illustrated with COVID-19

An Adaptive Susceptible-Infected-Removed-Vaccinated (A-SIRV) epidemic model with time-dependent transmission and removal rates is constructed for investigating the dynamics of an epidemic disease such as the COVID-19 pandemic. Real data of COVID-19 spread is used for the simultaneous identification of the unknown time-dependent rates and functions participating in the A-SIRV system. The inverse problem is formulated and solved numerically using the Method of Variational Imbedding, which reduces the inverse problem to a problem for minimizing a properly constructed functional for obtaining the sought values. To illustrate and validate the proposed solution approach, the present study used available public data for several countries with diverse population and vaccination dynamics—the World, Israel, The United States of America, and Japan.

Preventive control strategy on second wave of Covid-19 pandemic model incorporating lock-down effect

This study presents an optimal control strategy through a mathematical model of the Covid-19 outbreak without lock-down. The pandemic model analyses the lock-down effect without control strategy based on the current scenario of second wave data to control the rapid spread of the virus. The pandemic model has been discussed with respect to the basic reproduction number and stability analysis of disease-free and endemic equilibrium. A new optimal control problem with treatment is framed to minimize the vulnerable situation of the second wave. This system is applied to study the effects of vaccines and treatment controls. Numerical solutions and the graphical presentation of the results predict the fate of India’s second wave situation on account of the control strategy. Lastly, a comparative study with control and without control has been analysed for the exposed phase, infective phase, and recovery phase to understand the effectiveness of the controls. This model is used to estimate the total number of infected and active cases, deaths, and recoveries in order to control the disease using this system and studying the effects of vaccines and treatment controls.

How do the contaminated environment influence the transmission dynamics of COVID-19 pandemic?

COVID-19 is an infectious disease caused by the SARS-CoV-2 virus that first appeared in Wuhan city and then globally. The COVID-19 pandemic exudes public health and socio-economic burden globally. Mathematical modeling plays a significant role to comprehend the transmission dynamics and controlling factors of rapid spread of the disease. Researchers focus on the human-to-human transmission of the virus but the SARS-CoV-2 virus also contaminates the environment. In this study we proposed a nonlinear mathematical model for the COVID-19 pandemic to analyze the transmission dynamics of the disease in India. We have also incorporated the environment contamination by the infected individuals as the population density is very high in India. The model is fitted and parameterized using daily new infection data from India. Analytical study of the proposed COVID-19 model, including feasibility of critical points and their stability reveals that the infection-free steady state is stable if the basic reproduction number is less than unity otherwise the system shows significant outbreak. Numerical illustrations demonstrates that if the rate of environment contamination increased then the number of infected persons also increased. But if the environment is disinfected by sanitization then the number of infected persons cannot drastically increase.

A novel CO2-based demand-controlled ventilation strategy to limit the spread of COVID-19 in the indoor environment

Ventilation is of critical importance to containing COVID-19 contagion in indoor environments. Keeping the ventilation rate at high level is recommended by many guidelines to dilute virus-laden respiratory particles and mitigate airborne transmission risk. However, high ventilation rate will cause high energy use. Demand-controlled ventilation is a promising technology option for controlling indoor air quality in an energy-efficient manner. This paper proposes a novel CO2-based demand-controlled ventilation strategy to limit the spread of COVID-19 in indoor environments. First, the quantitative relationship is established between COVID-19 infection risk and average CO2 level. Then, a sufficient condition is proposed to ensure COVID-19 event reproduction number is less than 1 under a conservative consideration of the number of infectors. Finally, a ventilation control scheme is designed to make sure the above condition can be satisfied. Case studies of different indoor environments have been conducted on a testbed of a real ventilation system to validate the effectiveness of the proposed strategy. Results show that the proposed strategy can efficiently maintain the reproduction number less than 1 to limit COVID-19 contagion while saving about 30%-50% of energy compared with the fixed ventilation scheme. The proposed strategy offers more practical values compared with existing studies: it is applicable to scenarios where there are multiple infectors, and the number of infectors varies with time; it only requires CO2 sensors and does not require occupancy detection sensors. Since CO2 sensors are very mature and low-cost, the proposed strategy is suitable for mass deployment in most existing ventilation systems.

Geographic spread of COVID-19 and local economies: Heterogeneous effects by establishment size and industry

Using province-level establishments and employment data from the Korean Employment Insurance Database, this paper investigates how the regional spread of COVID-19 affects local businesses and unemployment by establishment size and industry. We find that the number of small establishments declines substantially after the COVID-19 pandemic through a decrease in new establishment creation and a surge in establishment closures. By contrast, large establishments are not affected significantly. Examining the numbers of unemployment benefits (UB) applicants, an indicator of unemployment, we find that the higher the rate of COVID-19 confirmed cases in a province, the higher the number of UB applicants, regardless of their previous workplace size. Our analysis of employment insurance subscribers further confirms that the regional spread of COVID-19 leads to a significant reduction in employment and job mobility in small establishments. Regarding industry heterogeneity in the COVID-19 effects, we find that local COVID-19 outbreaks affect local industries more through the reduction in establishment creation and new employment than through an increase in establishment closures. Industries that require face-to-face operations, such as lodging & restaurant, experience a substantial adverse impact in the early phase, and the impact also tends to last longer as COVID-19 situations prolong.

Spatialized epidemiological forecasting applied to Covid-19 pandemic at departmental scale in France

In this paper, we present a spatialized extension of a SIR model that accounts for undetected infections and recoveries as well as the load on hospital services. The spatialized compartmental model we introduce is governed by a set of partial differential equations (PDEs) defined on a spatial domain with complex boundary. We propose to solve the set of PDEs defining our model by using a meshless numerical method based on a finite difference scheme in which the spatial operators are approximated by using radial basis functions. Such an approach is reputed as flexible for solving problems on complex domains. Then we calibrate our model on the French department of Isère during the first period of lockdown, using daily reports of hospital occupancy in France. Our methodology allows to simulate the spread of Covid-19 pandemic at a departmental level, and for each compartment. However, the simulation cost prevents from online short-term forecast. Therefore, we propose to rely on reduced order modeling to compute short-term forecasts of infection number. The strategy consists in learning a time-dependent reduced order model with few compartments from a collection of evaluations of our spatialized detailed model, varying initial conditions and parameter values. A set of reduced bases is learnt in an offline phase while the projection on each reduced basis and the selection of the best projection is performed online, allowing short-term forecast of the global number of infected individuals in the department. The original approach proposed in this paper is generic and could be adapted to model and simulate other dynamics described by a model with spatially distributed parameters of the type diffusion-reaction on complex domains. Also, the time-dependent model reduction techniques we introduced could be leveraged to compute control strategies related to such dynamics.

Dynamical analysis of the infection status in diverse communities due to COVID-19 using a modified SIR model

In this article, we model and study the spread of COVID-19 in Germany, Japan, India and highly impacted states in India, i.e., in Delhi, Maharashtra, West Bengal, Kerala and Karnataka. We consider recorded data published in Worldometers and COVID-19 India websites from April 2020 to July 2021, including periods of interest where these countries and states were hit severely by the pandemic. Our methodology is based on the classic susceptible-infected-removed (SIR) model and can track the evolution of infections in communities, i.e., in countries, states or groups of individuals, where we (a) allow for the susceptible and infected populations to be reset at times where surges, outbreaks or secondary waves appear in the recorded data sets, (b) consider the parameters in the SIR model that represent the effective transmission and recovery rates to be functions of time and (c) estimate the number of deaths by combining the model solutions with the recorded data sets to approximate them between consecutive surges, outbreaks or secondary waves, providing a more accurate estimate. We report on the status of the current infections in these countries and states, and the infections and deaths in India and Japan. Our model can adapt to the recorded data and can be used to explain them and importantly, to forecast the number of infected, recovered, removed and dead individuals, as well as it can estimate the effective infection and recovery rates as functions of time, assuming an outbreak occurs at a given time. The latter information can be used to forecast the future basic reproduction number and together with the forecast on the number of infected and dead individuals, our approach can further be used to suggest the implementation of intervention strategies and mitigation policies to keep at bay the number of infected and dead individuals. This, in conjunction with the implementation of vaccination programs worldwide, can help reduce significantly the impact of the spread around the world and improve the wellbeing of people.

Mathematical modeling of COVID-19 pandemic in the context of sub-Saharan Africa: a short-term forecasting in Cameroon and Gabon

In this paper, we propose and analyse a compartmental model of COVID-19 to predict and control the outbreak. We first formulate a comprehensive mathematical model for the dynamical transmission of COVID-19 in the context of sub-Saharan Africa. We provide the basic properties of the model and compute the basic reproduction number $\mathcal {R}_0$ when the parameter values are constant. After, assuming continuous measurement of the weekly number of newly COVID-19 detected cases, newly deceased individuals and newly recovered individuals, the Ensemble of Kalman filter (EnKf) approach is used to estimate the unmeasured variables and unknown parameters, which are assumed to be time-dependent using real data of COVID-19. We calibrated the proposed model to fit the weekly data in Cameroon and Gabon before, during and after the lockdown. We present the forecasts of the current pandemic in these countries using the estimated parameter values and the estimated variables as initial conditions. During the estimation period, our findings suggest that $\mathcal {R}_0 \approx 1.8377 $ in Cameroon, while $\mathcal {R}_0 \approx 1.0379$ in Gabon meaning that the disease will not die out without any control measures in theses countries. Also, the number of undetected cases remains high in both countries, which could be the source of the new wave of COVID-19 pandemic. Short-term predictions firstly show that one can use the EnKf to predict the COVID-19 in Sub-Saharan Africa and that the second vague of the COVID-19 pandemic will still increase in the future in Gabon and in Cameroon. A comparison between the basic reproduction number from human individuals $\mathcal {R}_{0h}$ and from the SARS-CoV-2 in the environment $\mathcal {R}_{0v}$ has been done in Cameroon and Gabon. A comparative study during the estimation period shows that the transmissions from the free SARS-CoV-2 in the environment is greater than that from the infected individuals in Cameroon with $\mathcal {R}_{0h}$ = 0.05721 and $\mathcal {R}_{0v}$ = 1.78051. This imply that Cameroonian apply distancing measures between individual more than with the free SARS-CoV-2 in the environment. But, the opposite is observed in Gabon with $\mathcal {R}_{0h}$ = 0.63899 and $\mathcal {R}_{0v}$ = 0.39894. So, it is important to increase the awareness campaigns to reduce contacts from individual to individual in Gabon. However, long-term predictions reveal that the COVID-19 detected cases will play an important role in the spread of the disease. Further, we found that there is a necessity to increase timely the surveillance by using an awareness program and a detection process, and the eradication of the pandemic is highly dependent on the control measures taken by each government.

SIRVVD model-based verification of the effect of first and second doses of COVID-19/SARS-CoV-2 vaccination in Japan

As of August 2021, COVID-19 is still spreading in Japan. Vaccination, one of the key measures to bring COVID-19 under control, began in February 2021. Previous studies have reported that COVID-19 vaccination reduces the number of infections and mortality rates. However, simulations of spreading infection have suggested that vaccination in Japan is insufficient. Therefore, we developed a susceptible-infected-recovered-vaccination1-vaccination2-death model to verify the effect of the first and second vaccination doses on reducing the number of infected individuals in Japan; this includes an infection simulation. The results confirm that appropriate vaccination measures will sufficiently reduce the number of infected individuals and reduce the mortality rate.

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

The COVID-19 outbreak, which started in late December 2019 and rapidly spread around the world, has been accompanied by an unprecedented release of data on reported cases. Our objective is to offer a fresh look at these data by coupling a phenomenological description to the epidemiological dynamics. We use a phenomenological model to describe and regularize the reported cases data. This phenomenological model is combined with an epidemic model having a time-dependent transmission rate. The time-dependent rate of transmission involves changes in social interactions between people as well as changes in host-pathogen interactions. Our method is applied to cumulative data of reported cases for eight different geographic areas. In the eight geographic areas considered, successive epidemic waves are matched with a phenomenological model and are connected to each other. We find a single epidemic model that coincides with the best fit to the data of the phenomenological model. By reconstructing the transmission rate from the data, we can understand the contributions of the changes in social interactions (contacts between individuals) on the one hand and the contributions of the epidemiological dynamics on the other hand. Our study provides a new method to compute the instantaneous reproduction number that turns out to stay below 3.5 from the early beginning of the epidemic. We deduce from the comparison of several instantaneous reproduction numbers that the social effects are the most important factor in understanding the epidemic wave dynamics for COVID-19. The instantaneous reproduction number stays below 3.5, which 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 adjusting for higher confidence, it is sufficient to vaccinate 75-80% to eliminate COVID-19 in each state or country.

Inverse problem for adaptive SIR model: Application to COVID-19 in Latin America

This work presents a method for solving an Adaptive Susceptible-Infected-Removed (A-SIR) epidemic model with time-dependent transmission and removal rates. Available COVID-19 data as of March 2021 are used for identifying the rates from an inverse problem. The estimated rates are used to solve the adaptive SIR system for the spread of the infectious disease. This method simultaneously solves the problem for the time-dependent rates and the unknown functions of the A-SIR system. Presented results show the spread of COVID-19 in the World, Argentina, Brazil, Colombia, Dominican Republic, and Honduras. Comparisons of the reported affected by the disease individuals from the available real data and the values obtained with the A-SIR model demonstrate how well the model simulates the dynamic of the infectious disease.

An algorithm for the direct estimation of the parameters of the SIR epidemic model from the I(t) dynamics

The discrete SIR (Susceptible-Infected-Recovered) model is used in many studies to model the evolution of epidemics. Here, we consider one of its dynamics-the exponential decrease in infected cases I(t). By considering only the I(t) dynamics, we extract three parameters: the exponent of the initial exponential increase γ ; the maximum value I max ; and the exponent of the final decrease Γ . From these three parameters, we show mathematically how to extract all relevant parameters of the SIR model. We test this procedure on numerical data and then apply the methodology to real data received from the COVID-19 situation in France. We conclude that, based on the hospitalized data and the ICU (Intensive Care Unit) cases, two exponentials are found, for the initial increase and the decrease in I(t). The parameters found are larger than reported in the literature, and they are associated with a susceptible population which is limited to a sub-sample of the total population. This may be due to the fact that the SIR model cannot be applied to the covid-19 case, due to its strong hypotheses such as mixing of all the population, or also to the fact that the parameters have changed over time, due to the political initiatives such as social distanciation and lockdown.

Assessing the Impact of (Self)-Quarantine through a Basic Model of Infectious Disease Dynamics

We introduce a system of differential equations to assess the impact of (self-)quarantine of symptomatic infectious individuals on disease dynamics. To this end we depart from using the classic bilinear infection process, but remain within the framework of the mass-action assumption. From the mathematical point of view, the model we propose is interesting due to the lack of continuous differentiability at disease-free steady states, which implies that the basic reproductive number cannot be computed following established mathematical approaches for certain parameter values. However, we parametrise our mathematical model using published values from the COVID-19 literature, and analyse the model simulations. We also contrast model simulations against publicly available COVID-19 test data, focusing on the first wave of the pandemic during March-July 2020 in the UK. Our simulations indicate that actual peak case numbers might have been as much as 200 times higher than the reported positive test cases during the first wave in the UK. We find that very strong adherence to self-quarantine rules yields (only) a reduction of 22% of peak numbers and delays the onset of the peak by approximately 30-35 days. However, during the early phase of the outbreak, the impact of (self)-quarantine is much more significant. We also take into account the effect of a national lockdown in a simplistic way by reducing the effective susceptible population size. We find that, in case of a 90% reduction of the effective susceptible population size, strong adherence to self-quarantine still only yields a 25% reduction of peak infectious numbers when compared to low adherence. This is due to the significant number of asymptomatic infectious individuals in the population.

Current Status and Associated Factors of Depression and Anxiety Among the Chinese Residents During the Period of Low Transmission of COVID-19

Background: The outbreak of coronavirus disease 2019 (COVID-19) has contributed to depression and anxiety among the general population in China. The purpose of this study is to investigate the prevalence and associated factors of these psychological problems among Chinese adults during the period of low transmission, which could reflect the long-term depression and anxiety of the COVID-19 outbreak. Methods: A cross-sectional survey was conducted in China from 4 to 26 February 2021. Convenient sampling strategy was adopted to recruit participators. Participants were asked to filled out the questions that assessed questionnaire on the residents' depression and anxiety. Results: A total of 2,361 residents filled out the questionnaire. The mean age was 29.72 years (SD = 6.94) and majority of respondents were female (60.10%). Among the respondents, 421 (17.83%), 1470 (62.26%), and 470 (19.91%) were from eastern, central, and western China, respectively. 1704 (72.17%) consented COVID-19 information has been disclosed timely. 142 (6.01%) and 130 (5.51%) patients suffered from depression and anxiety symptoms. Furthermore, some influencing factors were found, including marital status, place of residence, employment status. Conclusion: This study revealed that anxiety and depression still are potential depression and anxiety for some residents, which suggested early recognition and initiation of interventions during the period of low transmission is still indispensable.

Modelling and forecasting of growth rate of new COVID-19 cases in top nine affected countries: Considering conditional variance and asymmetric effect

COVID-19 pandemic has affected more than a hundred fifty million people and killed over three million people worldwide over the past year. During this period, different forecasting models have tried to forecast time path of COVID-19 pandemic. Unlike the COVID-19 forecasting literature based on Autoregressive Integrated Moving Average (ARIMA) modelling, in this paper new COVID-19 cases were modelled and forecasted by conditional variance and asymmetric effects employing Generalized Autoregressive Conditional Heteroscedasticity (GARCH), Threshold GARCH (TARCH) and Exponential GARCH (EGARCH) models. ARMA, ARMA-GARCH, ARMA-TGARCH and ARMA-EGARCH models were employed for one-day ahead forecasting performance for April, 2021 and three waves of COVID-19 pandemic in nine most affected countries -USA, India, Brazil, France, Russia, UK, Italy, Spain and Germany. Empirical results show that ARMA-GARCH models have better forecast performance than ARMA models by modelling both the conditional heteroskedasticity and the heavy-tailed distributions of the daily growth rate of the new confirmed cases; and asymmetric GARCH models show mixed results in terms of reducing the root mean squared error (RMSE).

Dynamics of partially mitigated multi-phasic epidemics at low susceptible depletion: phases of COVID-19 control in Italy as case study

To mitigate the harmful effects of the COVID-19 pandemic, world countries have resorted - though with different timing and intensities - to a range of interventions. These interventions and their relaxation have shaped the epidemic into a multi-phase form, namely an early invasion phase often followed by a lockdown phase, whose unlocking triggered a second epidemic wave, and so on. In this article, we provide a kinematic description of an epidemic whose time course is subdivided by mitigation interventions into a sequence of phases, on the assumption that interventions are effective enough to prevent the susceptible proportion to largely depart from 100% (or from any other relevant level). By applying this hypothesis to a general SIR epidemic model with age-since-infection and piece-wise constant contact and recovery rates, we supply a unified treatment of this multi-phase epidemic showing how the different phases unfold over time. Subsequently, by exploiting a wide class of infectiousness and recovery kernels allowing reducibility (either to ordinary or delayed differential equations), we investigate in depth a low-dimensional case allowing a non-trivial full analytical treatment also of the transient dynamics connecting the different phases of the epidemic. Finally, we illustrate our theoretical results by a fit to the overall Italian COVID-19 epidemic since March 2020 till February 2021 i.e., before the mass vaccination campaign. This show the abilities of the proposed model in effectively describing the entire course of an observed multi-phasic epidemic with a minimal set of data and parameters, and in providing useful insight on a number of aspects including e.g., the inertial phenomena surrounding the switch between different phases.

SUIHTER: a new mathematical model for COVID-19. Application to the analysis of the second epidemic outbreak in Italy

The COVID-19 epidemic is the latest in a long list of pandemics that have affected humankind in the last century. In this paper, we propose a novel mathematical epidemiological model named SUIHTER from the names of the seven compartments that it comprises: susceptible uninfected individuals (S), undetected (both asymptomatic and symptomatic) infected (U), isolated infected (I), hospitalized (H), threatened (T), extinct (E) and recovered (R). A suitable parameter calibration that is based on the combined use of the least-squares method and the Markov chain Monte Carlo method is proposed with the aim of reproducing the past history of the epidemic in Italy, which surfaced in late February and is still ongoing to date, and of validating SUIHTER in terms of its predicting capabilities. A distinctive feature of the new model is that it allows a one-to-one calibration strategy between the model compartments and the data that are made available daily by the Italian Civil Protection Department. The new model is then applied to the analysis of the Italian epidemic with emphasis on the second outbreak, which emerged in autumn 2020. In particular, we show that the epidemiological model SUIHTER can be suitably used in a predictive manner to perform scenario analysis at a national level.

Underdetection in a stochastic SIR model for the analysis of the COVID-19 Italian epidemic

We propose a way to model the underdetection of infected and removed individuals in a compartmental model for estimating the COVID-19 epidemic. The proposed approach is demonstrated on a stochastic SIR model, specified as a system of stochastic differential equations, to analyse data from the Italian COVID-19 epidemic. We find that a correct assessment of the amount of underdetection is important to obtain reliable estimates of the critical model parameters. The adaptation of the model in each time interval between relevant government decrees implementing contagion mitigation measures provides short-term predictions and a continuously updated assessment of the basic reproduction number.

High health expenditures and low exposure of population to air pollution as critical factors that can reduce fatality rate in COVID-19 pandemic crisis: a global analysis

One of the problems hardly clarified in Coronavirus Disease 2019 (COVID-19) pandemic crisis is to identify factors associated with a lower mortality of COVID-19 between countries to design strategies to cope with future pandemics in society. The study here confronts this problem by developing a global analysis based on more than 160 countries. This paper proposes that Gross Domestic Product (GDP) per capita, healthcare spending and air pollution of nations are critical factors associated with fatality rate of COVID-19. The statistical evidence seems in general to support that countries with a low average COVID-19 fatality rate have high expenditures in health sector >7.5% of GDP, high health expenditures per capita >$2,300 and a lower exposure of population to days exceeding safe levels of particulate matter (PM2.5). Another relevant finding here is that these countries have lower case fatality rates (CFRs) of COVID-19, regardless a higher percentage of population aged more than 65 years. Overall, then, this study finds that an effective and proactive strategy to reduce the negative impact of future pandemics, driven by novel viral agents, has to be based on a planning of enhancement of healthcare sector and of environmental sustainability that can reduce fatality rate of infectious diseases in society.

Estimation of Undetected Asymptomatic COVID-19 Cases in South Korea Using a Probabilistic Model

Increasing evidence shows that many infections of COVID-19 are asymptomatic, becoming a global challenge, since asymptomatic infections have the same infectivity as symptomatic infections. We developed a probabilistic model for estimating the proportion of undetected asymptomatic COVID-19 patients in the country. We considered two scenarios: one is conservative and the other is nonconservative. By combining the above two scenarios, we gave an interval estimation of 0.0001-0.0027 and in terms of the population, 5200-139,900 is the number of undetected asymptomatic cases in South Korea as of 2 February 2021. In addition, we provide estimates for total cases of COVID-19 in South Korea. Combination of undetected asymptomatic cases and undetected symptomatic cases to the number of confirmed cases (78,844 cases on 2 February 2021) shows that 0.17-0.42% (89,244-218,744) of the population have COVID-19. In conclusion, to control and understand the true ongoing reality of the pandemic, it is of outermost importance to focus on the ratio of undetected asymptomatic cases in the total population.

The Quixotic Task of Forecasting Peaks of COVID-19: Rather Focus on Forward and Backward Projections

Over the last months, mathematical models have been extensively used to help control the COVID-19 pandemic worldwide. Although extremely useful in many tasks, most models have performed poorly in forecasting the pandemic peaks. We investigate this common pitfall by forecasting four countries' pandemic peak: Austria, Germany, Italy, and South Korea. Far from the peaks, our models can forecast the pandemic dynamics 20 days ahead. Nevertheless, when calibrating our models close to the day of the pandemic peak, all forecasts fail. Uncertainty quantification and sensitivity analysis revealed the main obstacle: the misestimation of the transmission rate. Inverse uncertainty quantification has shown that significant changes in transmission rate commonly precede a peak. These changes are a key factor in forecasting the pandemic peak. Long forecasts of the pandemic peak are therefore undermined by the lack of models that can forecast changes in the transmission rate, i.e., how a particular society behaves, changes of mitigation policies, or how society chooses to respond to them. In addition, our studies revealed that even short forecasts of the pandemic peak are challenging. Backward projections have shown us that the correct estimation of any temporal change in the transmission rate is only possible many days ahead. Our results suggest that the distance between a change in the transmission rate and its correct identification in the curve of active infected cases can be as long as 15 days. This is intrinsic to the phenomenon and how it affects epidemic data: a new case is usually only reported after an incubation period followed by a delay associated with the test. In summary, our results suggest the phenomenon itself challenges the task of forecasting the peak of the COVID-19 pandemic when only epidemic data is available. Nevertheless, we show that exciting results can be obtained when using the same models to project different scenarios of reduced transmission rates. Therefore, our results highlight that mathematical modeling can help control COVID-19 pandemic by backward projections that characterize the phenomena' essential features and forward projections when different scenarios and strategies can be tested and used for decision-making.

Forecasting COVID-19 Confirmed Cases Using Empirical Data Analysis in Korea

From November to December 2020, the third wave of COVID-19 cases in Korea is ongoing. The government increased Seoul's social distancing to the 2.5 level, and the number of confirmed cases is increasing daily. Due to a shortage of hospital beds, treatment is difficult. Furthermore, gatherings at the end of the year and the beginning of next year are expected to worsen the effects. The purpose of this paper is to emphasize the importance of prediction timing rather than prediction of the number of confirmed cases. Thus, in this study, five groups were set according to minimum, maximum, and high variability. Through empirical data analysis, the groups were subdivided into a total of 19 cases. The cumulative number of COVID-19 confirmed cases is predicted using the auto regressive integrated moving average (ARIMA) model and compared with the actual number of confirmed cases. Through group and case-by-case prediction, forecasts can accurately determine decreasing and increasing trends. To prevent further spread of COVID-19, urgent and strong government restrictions are needed. This study will help the government and the Korea Disease Control and Prevention Agency (KDCA) to respond systematically to a future surge in confirmed cases.

The europe second wave of COVID-19 infection and the Italy "strange" situation

At the end of February 2020 COVID-19 infection appeared in Italy, with consequent diffusion, in few weeks, in almost all the Europe. Despite that human-to-human is the recognized main virus transmission way, several authors supposed pollution-to-human mechanisms to justify the appearance of contagious in Italy. However, these works often suffered of a lack of analysis of possible overlapping of different variables, other than only environmental ones. After a decreasing of detected cases in summer, Europe faced with the appearance of a COVID-19 second wave. In this context the Italy situation appeared to be "strange". Indeed, compared with the other selected Countries (France, Germany, UK, and Spain), the Italian infection cases resulted to be lower, in the same analysed period. This work is devoted to find a possible justification of the unexpected situation found in Italy. A comparison of the imposed restrictions in the considered Countries allows to highlight that some policies result more effective to limit the virus spread. This clearly shows that the imposed constraints and the people capacities to receipt them are fundamental parameters that must be always accounted in the determination of the virus expansion. The lesson provided by Italy should be achieved by other member states where the COVID-19 sanitary crisis results to be worse. It is evident that the re-opening of ordinary activities involving people interactions, in Autumn, may contribute to promote a larger SARS-CoV-2 diffusion also in Italy. Author strongly highlights that pollution-to-human transmission mechanisms cannot be proposed whiteout considering the complexity of human-to-human interactions, that can be modified by imposed restrictions. It is fundamental to understand that a more precise acknowledge of the variables that should be considered in model predictions, instead of a need of more precise point prediction, will contribute to increase the reliability and the comprehension of the virus diffusion mechanisms, that is fundamental to face this pandemic period.

Clarifying predictions for COVID-19 from testing data: The example of New York State

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.

Epidemiological Forecasting with Model Reduction of Compartmental Models. Application to the COVID-19 Pandemic

Simple Summary

Using tools from the reduced order modeling of parametric ODEs and PDEs, including a new positivity-preserving greedy reduced basis method, we present a novel forecasting method for predicting the propagation of an epidemic. The method takes a collection of highly detailed compartmental models (with different initial conditions, initial times, epidemiological parameters and numerous compartments) and learns a model with few compartments which best fits the available health data and which is used to provide the forecasts. We illustrate the promising potential of the approach to the spread of the current COVID-19 pandemic in the case of the Paris region during the period from March to November 2020, in which two epidemic waves took place.

Abstract

We propose a forecasting method for predicting epidemiological health series on a two-week horizon at regional and interregional resolution. The approach is based on the model order reduction of parametric compartmental models and is designed to accommodate small amounts of sanitary data. The efficiency of the method is shown in the case of the prediction of the number of infected people and people removed from the collected data, either due to death or recovery, during the two pandemic waves of COVID-19 in France, which took place approximately between February and November 2020. Numerical results illustrate the promising potential of the approach.

Epidemic Dynamics via Wavelet Theory and Machine Learning with Applications to Covid-19

We introduce the concept of epidemic-fitted wavelets which comprise, in particular, as special cases the number I(t) of infectious individuals at time t in classical SIR models and their derivatives. We present a novel method for modelling epidemic dynamics by a model selection method using wavelet theory and, for its applications, machine learning-based curve fitting techniques. Our universal models are functions that are finite linear combinations of epidemic-fitted wavelets. We apply our method by modelling and forecasting, based on the Johns Hopkins University dataset, the spread of the current Covid-19 (SARS-CoV-2) epidemic in France, Germany, Italy and the Czech Republic, as well as in the US federal states New York and Florida.