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The model descibes the epidemic dynamics of Covid-19 in a population after vaccination. Using the maximum principale, our goal is to prove the existence of an optimal strategy such that it minimize the number of infected people after vaccination. Finally, some numerical results are provided.

On both sides of the Atlantic, in Anglo-Saxon countries, the issue of excess mortality due to Covid-19 among members of minorities has emerged as a central social justice issue. Outside the Anglo-Saxon countries, where race and ethnicity are generally recorded, it is difficult to address this issue. However, in France, data for the period up to the end of confinement, mentioning country of birth and place of death, from "état-civil" files, allow comparisons to be made on the determinants of the severity of Covid-19 integrating ethnicity. Regression analyses based on the difference in death counts between the spring of 2020 and the same period of previous years, show that the interweaving of health status, household size and ethnicity accurately reflects the disparities between departmental mortality rates due to Covid-19. People born in Black Africa clearly appear to be in a worse position than those born in the Maghreb, in Asian and European countries, not to mention the natives, in terms of risk of death.

The COVID-19 outbreak offers a rich case study of government’s emergency response. As such, it is a test bed for risk research and regulatory theories in a world increasingly shaped by transboundary, uncertain manufactured and natural risks.This introductory essay to the special issue of the European Journal of Risk Regulation attempts at providing an initial analysis of the surprisingly uncoordinated, at times unscientific, response to an essentially foreseeable event like a novel coronavirus (nCoV) in a geopolitically shattered world.It warns that COVID-19 may go down in history as yet another major disaster occurrence with no learnings attached. Yet, as new transboundary disasters – from bioterrorism to climate change – loom on the horizon, neither the world nor risk regulation, as a discipline and practice of government, can hardly afford to let another crisis go wasted.

Europe is now considered as the epicenter of the SARS-CoV-2 pandemic, France being among the most impacted country. In France, there is an increasing concern regarding the capacity of the healthcare system to sustain the outbreak, especially regarding intensive care units (ICU). The aim of this study was to estimate the dynamics of the epidemic in France, and to assess its impact on healthcare resources for each French metropolitan Region. We developed a deterministic, age-structured, Susceptible-Exposed-Infectious-Removed (SEIR) model based on catchment areas of each COVID-19 referral hospitals. We performed one month ahead predictions (up to April 14, 2020) for three different scenarios (R0=1.5, R0=2.25, R0=3), where we estimated the daily number of COVID-19 cases, hospitalizations and deaths, the needs in ICU beds per Region and the reaching date of ICU capacity limits. At the national level, the total number of infected cases is expected to range from 22,872 in the best case (R0=1.5) to 161,832 in the worst case (R0=3), while the total number of deaths would vary from 1,021 to 11,032, respectively. At the regional level, all ICU capacities may be overrun in the worst scenario. Only seven Regions may lack ICU beds in the mild scenario (R0=2.25) and only one in the best case. In the three scenarios, Corse may be the first Region to see its ICU capacities overrun. The two other Regions, whose capacity will be overrun shortly after are Grand-Est and Bourgogne-Franche-Comté. Our analysis shows that, even in the best case scenario, the French healthcare system will very soon be overwhelmed. While drastic social distancing measures may temper our results, a massive reorganization leading to an expansion of French ICU capacities seems to be necessary to manage the coming wave of critically affected COVID-19 patients.

Uprising in China, the global COVID-19 epidemic soon started to spread out in Europe. As no medical treatment was available, it became urgent to design optimal non-pharmaceutical policies. With the help of a SIR model, we contrast two policies, one based on herd immunity (adopted by Sweden and the Netherlands), the other based on ICU capacity shortage. Both policies led to the danger of a second wave. Policy efficiency corresponds to the absence or limitation of a second wave. The aim of the paper is to measure the efficiency of these policies using statistical models and data. As a measure of efficiency, we propose the ratio of the size of two observed waves using a double sigmoid model coming from the biological growth literature. The Oxford data set provides a policy severity index together with observed number of cases and deaths. This severity index is used to illustrate the key features of national policies for ten European countries and to help for statistical inference. We estimate basic reproduction numbers, identify key moments of the epidemic and provide an instrument for comparing the two reported waves between January and October 2020. We reached the following conclusions. With a soft but long lasting policy, Sweden managed to master the first wave for cases thanks to a low R 0 , but at the cost of a large number of deaths compared to other Nordic countries and Denmark is taken as an example. We predict the failure of herd immunity policy for the Netherlands. We could not identify a clear sanitary policy for large European countries. What we observed was a lack of control for observed cases, but not for deaths.

In this Note, I present an original dynamic model of progression of Covid-19 epidemic in France, the so-called HOPE model, which remains relatively simple. Our model follows at the best four reliable indicators: the number of patients in Hospitals and in Intensive Care Units (ICU's), the Outflux from Hospitals and the number of Deaths which are reported daily by the French Public Healthcare system. Then, we give results about the influence of the complete lockdown measures taken by the French government on March 17, 2020, initially for 15 days, then for 30 days and now until May 11, 2020 but perhaps further. We show the tremendous impact of the general lockdown on the infectious tsunami to avoid the huge natural disaster which should occur if it was not applied. Indeed, the number of deaths is found divided by the factor 120 by applying a complete lockdown of 60 days with an efficiency ratio evaluated to 75%. We discuss this impact with respect of the efficiency and/or the duration of the containment. In particular, we show that a small effort of +1% in the efficiency of the lockdown saves 600 human lives; reversely, a small relaxation of −1% in the lockdown respect costs 600 deaths more. Next, we investigate the outbreak of an uncontrolled secondary wave of infection after the lockdown. Consequently, we show that the "stop and go" strategy is probably not a reasonable and sustainable scenario but rather a real crash test for the Healthcare system. Finally, we propose the suppression strategy called "successive damping cascade" after the general lockdown which allows the efficiency ratio to go progressively to zero within several less and less controlled secondary waves.

1st lines: In the upcoming European Council on July 17 and 18, EU member states will fight for a compromise on the European Commission’s main project to tackle the economic fallout of the Covid-19 crisis across Europe: a new 7-year EU budget propped up with a temporary Recovery Instrument (Next Generation EU) amounting to EUR 750 bn of jointly issued debt and to be passed on to EU countries as grants and loans. It is one of the most ambitious in a long line of proposals for European debt mutualisation.While joint borrowing can carry a lot of advantages, debt mutualisation has always been very controversial. Confrontations between those countries supposedly benefiting and losing from mutualising debt have repeatedly centered on the legitimate balance of solidarity and responsibility that such debt implies. Democratic legitimacy in solidarity-responsibility arrangements can be achieved when they can deliver in terms of output legitimacy (being effective in economic terms), input legitimacy (ensuring sufficient room for domestic politics in deciding national policy trajectories) and throughput legitimacy (being run in a transparent and accountable manner).

The European response to COVID-19 has revealed an inconvenient truth. Despite having integrated public health concerns across all its policies – be it agriculture, consumer protection, or security –, the Union cannot directly act to save people’s lives. Only member states can do so. Yet when they adopted unilateral measures to counter the spread of the virus, those proved not only ineffective but also disruptive on vital supply chains, by ultimately preventing the flow of essential goods and people across the Union. These fragmented efforts in tackling cross-border health threats have almost immediately prompted political calls for the urgent creation of a European Health Union. Yet this call raises more questions than answers. With the aim to offer a rigorous and timely blueprint to decision-makers and the public at large, this Special Issue of the European Journal of Risk Regulation contextualizes such a new political project within the broader constitutional and institutional framework of EU public health law and policy. By introducing the Special, this paper argues that unless the envisaged Health Union will tackle the root causes of what prevented the Union from effectively responding to COVID19 – the divergent health capacity across the Union –, it might fall short of its declared objective of strengthening the EU’resilience for cross-border health threats.

The current outbreak of COVID-19 has called renewed attention to the need for sound statistical analysis for monitoring mortality patterns and trends over time. Excess mortality has been suggested as the most appropriate indicator to measure the overall burden of the pandemic on mortality. As such, excess mortality has received considerable interest during the first months of the COVID-19 pandemic. Previous approaches to estimate excess mortality are somewhat limited, as they do not include sufficiently long-term trends, correlations among different demographic and geographic groups, and the autocorrelations in the mortality time series. This might lead to biased estimates of excess mortality, as random mortality fluctuations may be misinterpreted as excess mortality. We present a blend of classical epidemiological approaches to estimating excess mortality during extraordinary events with an established demographic approach in mortality forecasting, namely a Lee-Carter type model, which covers the named limitations and draws a more realistic picture of the excess mortality. We illustrate our approach using weekly age- and sex-specific mortality data for 19 countries and the current COVID-19 pandemic as a case study. Our proposed model provides a general framework that can be applied to future pandemics as well as to monitor excess mortality from specific causes of deaths.

On 12 March 2020, the sharp fell of U.S. crude oil price to 30 dollars was explained by the outspreads of coronavirus pandemic and the OPEC's inability to reach a production quota agreement. We employ the structural VAR model with time-varying coefficients and stochastic volatility (TVP-SVAR model) developed by Primiceri (2005) to asses the impact of COVID-19 shocks on the energy futures markets, particularly on crude oil and natural gas S&P GS Indexes. The findings confirm that energy commodities S&P GS Indexes respond to COVID-19 shock that varying over time due to fundamentals factors as well as behavioral and psychological factors.