Modeling the propagation of Covid-19.
Monday 18 to Wednesday 20 May 2020 – videoconference
- Patrice Bourdelais (EHESS)
Mapping the course of an epidemic: the example of two cholera epidemics in France (1832 and 1854)
Abstract : The Covid 19 epidemic is a reminder of the difficulty of producing robust data on the number of deaths due to this deseasee. Nothing seems to have changed in this respect since the 19th century! I will give the example of how we managed to map, using a simple indicator, the month-by-month progress of two cholera epidemics in France (1832 and 1854).
- Laura Di Domenico & Vittoria Colizza (EPIcx lab, INSERM, Sorbonne Université)
Expected impact of lockdown on COVID-19 epidemic in Île-de-France and possible exit strategies
- Gabriel Dulac-Arnold (Google Research) & Jean-Pierre Nadal (CAMS & LPENS, CNRS et EHESS)
with Julie Josse (Inria), Antoine Kimmoun (CHRU Nancy), Olivier Teboul (Google Research), and all the ICUBAM team: Laurent Bonnasse-Gahot, Maxime Dénès, Sertan Girgin, François Husson, Valentin Iovene, François Landes, Romain Primet, Frederico Quintao, Pierre Guillaume Raverdy, Vincent Rouvreau, Roman Yurchak.
Intensive Care Unit Bed Availability Monitoring and Modelling during the COVID-19 Epidemic in the Grand Est region of France
Abstract : Reliable information is an essential component for responding to the COVID-19 epidemic, especially regarding the availability of critical care beds (CCBs). This talk presents a (still ongoing) project, with three components : a) ICUBAM, for « Intensive Care Unit (ICU) Bed Availability Monitor », a tool which both collects and visualizes information on CCB availability entered directly by intensivists; b) An analysis of CCB availability and ICU admissions and outcomes using data collected by ICUBAM during a 6-week period in the hard-hit Grand Est région of France, and c) Explanatory and predictive models adapted to CCB availability prediction, and fitted to availability information collected by ICUBAM.
ICUBAM was brought online March 25, and is currently being used in the Grand Est région by 109 intensivists representing 40 ICUs (95\% of ICUs). Our analysis of data describes the evolution and extent of the COVID-19 health crisis in the Grand Est région. We also present how data ingested by ICUBAM can be used to anticipate CCB shortages and predict future admissions. Most importantly, we demonstrate the importance of having a cross-functional team involving physicians, statisticians, computer scientists and physicists working both with first-line medical responders and local health agencies. This allowed us to quickly implement effective tools to assist in critical decision-making processes.
Ref : ICUBAM open source software : https://icubam.github.io/
- Luca Ferretti (Large data Institute et Bio-statistics, Oxford)
Epidemic control of COVID-19 through rapid contact tracing: the case for a mobile app-based solution
Abstract: Mobile apps for contact tracing appear prominently in the current public debate. Their implications in terms of privacy and data security are under intense scrutiny by cybersecurity experts, lawyers and politicians, as well as the general public. Unfortunately, the most important questions are often absent from this debate: what is the epidemiological rationale behind the suggestion to deploy such a risky tool? Which role would these apps play in the control of the COVID-19 epidemic, and why are they so relevant? In this talk, I will present the scientific arguments underpinning the answers. I will summarize our understanding of COVID-19 epidemiology and SARS-CoV-2 transmission and I will discuss the challenges of different containment strategies for this epidemic. In this framework, I will highlight how speed and efficiency are the main determinants of the effectiveness of contact tracing in controlling the epidemic, and why digital solutions are the most promising ones. I will also discuss current limitations and challenges of both app-based approaches and their alternatives.
- Marie Gaille (senior research in philosophy, SPHERE, CNRS-University of Paris)
To be tracking or not tracking, that is the question … or not?
- Marino Gatto (Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano)
joint work with: Enrico Bertuzzo (2,3), Lorenzo Mari(1), Damiano Pasetto (2), Stefano Miccoli (4), Renato Casagrandi (1),, and Andrea Rinaldo (5,6)
1. Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, 20133 Milano IT
2. Dipartimento di Scienze Ambientali, Informatica e Statistica, Università Ca’ Foscari, 30172 Venezia IT
3. Science of Complexity Research Unit, European Centre for Living Technology, 30123 Venice IT
4. Dipartimento di Meccanica, Politecnico di Milano, 20156 Milano IT
5. Laboratory of Ecohydrology, École Polytechnique Fédérale de Lausanne, 1015 Lausanne CH
6. Dipartimento ICEA, Università di Padova, 35131 Padova IT
The routes of COVID-19 in Italy: past and future scenarios
Abstract: Italy has been the first European country to be ravaged by the spread of coronavirus disease 2019 (COVID-19). The spatial signature of the disease diffusion from the initial foci located in northern Italy has been clear from the very beginning. To include this important feature, we have developed a spatially explicit model of the epidemic. It is a metacommunity Susceptible–Exposed–Infected–Recovered (SEIR)- like transmission model that includes a network of 107 provinces connected by mobility at high resolution, and the critical contribution of pre-symptomatic and asymptomatic transmission. The dramatic and devastating increase of hospitalized people prompted drastic measures for transmission containment. We have examined the effects of these interventions, by including the implementation of the sequence of restrictions up to the beginning of May. We employ Bayesian methods to estimate the model parameters. We have first drawn retrospective scenarios to estimate the number of averted hospitalizations due to the containment measures. These total to about 200,000 individuals (as of March 25, 2020). Also, we have estimated that the median of the total number of infections was approximately 730, 000 individuals at that date. Subsequently, parameters have been updated until the end of April 2020, leading us to estimate a large reduction in the disease transmission rate in each province, with the ratio of the May 1st transmission rate to the initial rate ranging between 0.3 and 0.4 depending on location. Based on the updated parameters we have projected scenarios for the relaxation of the lockdown after May 4th. The effects of lifting the lockdown have been estimated by comparison with the so-called baseline scenario, that is, the expected unfolding of the outbreak if the strict containment measures enforced up to May 3rd were kept in place indefinitely. If the relaxation of containment measures resulted in a 40% increase of the transmission rate, this would yield an epidemic curve that shows a major rebound, larger than the previous peaks in most regions of Italy. We then estimate the isolation effort required to prevent a resurgence of the outbreak and track the baseline scenario, should such an increase of transmission actually materialize in the next weeks. It amounts to approximately isolating every day 5.5% of exposed and highly infectious pre-symptomatic individuals. We discuss the feasibility of this measure via testing and contact tracing. A sensitivity analysis has also been run to assess the influence of the largely uncertain percentage of asymptomatic infectious individuals.
- Quentin Griette and Pierre Magal (Institut de Mathématiques de Bordeaux)
Understanding unreported cases in the COVID-19 epidemic outbreak and the importance of major public health interventions
Abstract: In the first part of this presentation we develop a mathematical model to provide epidemic predictions for the COVID-19 epidemic in China. We use reported case data from the Chinese Center for Disease Control and Prevention and the Wuhan Municipal Health Commission to parameterize the model. From the parameterized model we identify the number of unreported cases. We then use the model to project the epidemic forward with varying level of public health interventions. The model predictions emphasize the importance of major public health interventions in controlling COVID-19 epidemics. The second part of the presentation will be devoted to an age structured model applied to data from Japan.
- Marc Lavielle (Inria, CMAP Ecole Polytechnique)
Modelling the COVID 19 pandemic requires a model… but also data!
Abstract : We propose to build a SIR-type model for the Covid-19 data provided by the Johns-Hopkins University. The data available for each country are the daily number of confirmed cases and the daily number of deaths. The model is adapted in order to fit the data at an aggregated level like a country. In other words, the parameters of the model change from country to country to reflect differences in dynamics.
In particular, the model integrates a time-dependent transmission rate, whose variations can be thought to be related to the public health measures taken by the country in question. A piecewise linear model is used for the transmission rate to take into account these possible variations.
The proposed model may seem simple, but it should be understood that it does not pretend to describe the spread of the pandemic in a precise and detailed manner. Its role is to adjust the available data: its complexity is therefore adjusted to the amount of information available in the data. Indeed very few parameters are needed to properly describe the outcome of interest, and the prediction proves stable over time.
The model, the parameter estimation algorithm, the method for model selection as well as several plotting routines have been implemented in an interactive, easy to use, web application that allows to visualize the data and the fitted model for several countries (http://shiny.webpopix.org/covidix/app2/). The data used in this application are updated frequently in order to be able to follow on a day-to-day basis what the model predicts for several countries.
- Gabriel Leung (Chair of Population Health Medicine, University of Hong-Kong)
Research insights about COVID-19 from Hong Kong
- Samuel Nordmann (Tel-Aviv University)
Joint work with Henri Berestycki and Luca Rossi.
Activity/susceptibility systems: a general class of models for the propagation of epidemics, social unrest and other collective behaviors
Abstract : A considerable number of studies are devoted to the introduction and analysis of variants of the SIR epidemiology models. Similar models are also used to describe collective behaviors in other contexts, such as the dynamics of riots, the adoption of a technology or a belief, etc. The use of epidemiology models to describe such social phenomena is based on the analogy between the
mechanisms of contagion and social imitation. In turn, this analogy also denotes that epidemics are essentially a social phenomenon.
Given the variety of models considered in the literature, an important task is to identify a general paradigm and to provide mathematical tools to analyze it. In this talk, we propose a large class of Reaction-Diffusion systems that aims at unifying and generalizing classical epidemiology models. Our model involves two quantities, the level of activity u, and a field of susceptibility v, which play asymmetric roles: u is thought of as the actual observed or explicit quantity while v is an implicit field that modulates the growth of u. Other classical models fit our framework: the prey/predator system, the Bass model in marketing, the equation for a flame propagation, etc.
We highlight a threshold phenomenon in terms of the initial level of susceptibility v0. This generalizes the well known threshold on the reproductive number R0 in the classical SIR model. We also propose general results about the spatial propagation.</p
- Lulla Opatowski (Univ. de Versailles Saint Quentin / Institut Pasteur / Inserm)
Modelling sars-cov2 transmission in the French community and hospitals
Abstract: The emergence of SARS-CoV-2 in December 2019 in China and its worldwide dissemination has become a major public health priority. Most countries have now reported confirmed cases on their territories and the outbreak was declared a Public Health Emergency of International Concern on January 30, 2020 by WHO. In France, the first cases were reported in January 2020. Since then, the virus has spread in the community, leading to the implementation of unprecedented measures at the population level including school closure and population confinement. In this context, healthcare institutions are confronted to major challenges. First the community spread is leading to a large demand in available beds and to a saturation in hospitals dedicated to COVID-19 patients, particularly in intensive care units. Second, the outbreak and its managements are causing a large-scale disorganization of the entire healthcare system. Third, healthcare settings have been shown to be hotspots of transmission of coronaviruses, notably due to the high density of contacts. I will present a series of modelling works addressing these questions.
- Gilles Pialoux (Head of the Infectious Diseases Unit, Tenon Hospital, France)
After the first wave of the COVID-19 crisis can the health care worker still believe in modeling? – Talk in French with slides in English
- Andrea Pugliese (University of Trento)
Inferring time course of infections from proxy aggregated data: problems and perspectives
Abstract: Inferring the time course of COVID-19 infections is one of the essential information in order to establish the effect of containment strategies, especially now that many restrictions are being lifted in most countries. Available aggregated data can easily provide running estimates of the epidemic course. Because of the delays between infections and events (case diagnosis, hospitalizations, deaths) that are reported, it is necessary to `back-calculate’ from reported data to estimated infection events. The method, introduced many years ago for HIV-AIDS, relies on good estimates of the distribution of the delays between infection and the observed events. Then, assuming that the epidemic follows a simple SIR model with a known serial interval, parameters can be estimated through maximum likelihood (or other methods), obtaining an estimate of time-varying contact rates. I will show the application of the method to data from Italy and several of its regions, relying mainly on deaths and hospitalizations for the initial period, and on reported cases more recently.
- Jean-Michel Roquejoffre (Institut de Mathématiques, Université Paul Sabatier, Toulouse, et CAMS, EHESS, Paris
Joint work with H. Berestycki and L. Rossi.
Propagation of epidemics on lines of fast diffusion
Abstract: It has been observed that epidemics can travel along lines of communications, such as roads. The curent COVID-19 epidemics is no exception to this rule, as an enhancement of is propagation by major roads has been reported in the North of Italy. The goal of this talk is to discuss a new and simple mathematical model that we have proposed, and that exhibits this effect.
The model consists of a classical SIR model with diffusion, to which an additional compartment is added, formed by the infected individuals travelling on a line of fast diffusion. Exchanges between individuals on the line and in the rest of the domain are taken into account.
The analysis of this model shows that the line may dramatically enhance the propagation of the epidemics, even when the basic reproduction number R0 is close to 1. It also displays motr subtle qualitative features of the final state, that will also be discussed.
- Lionel Roques (Ecology, INRAE, Avignon)
Estimating the infection fatality ratio from COVID-19 and the impact of the lockdown in France
Abstract: The number of screening tests carried out in France and the methodology used to target the patients tested do not allow for a direct computation of the actual number of cases and the infection fatality ratio (IFR). Our first objective is to estimate the actual IFR based on early data in France (before the lockdown). Our second objective is to estimate the effect of the lockdown on the epidemic dynamics and the actual number of infected cases by the beginning of May in France. We develop a `mechanistic-statistical’ approach coupling a SIR epidemiological model describing the unobserved epidemiological dynamics, a probabilistic model describing the data acquisition process and a statistical inference method. We find an IFR in France of 0.5% (95%-CI: 0.3–0.8) based on hospital death counting data. Adjusting for the number of deaths in nursing homes, we obtain an IFR of 0.8% (95%-CI: 0.45–1.25). Regarding the effect of the lockdown, we obtain a reduction by a factor 7 of the effective reproduction number (Re=0.5), compared to the estimates carried out in France at the early stage of the epidemic (R0=3.2). We find a fraction of 4% of the total French population that is infected by the beginning of May. This proportion is seemingly too low to reach herd immunity at the country scale. Thus, even if the lockdown strongly mitigated the first epidemic wave, keeping a low value of Re is crucial to avoid an uncontrolled second wave (initiated with much more infectious cases than the first wave) and to hence avoid the saturation of hospital facilities.
BioSP COVID-19 webpage: http://covid19.biosp.org
- Giovanni Sebastiani (Statistics, IAC-CNR and La Sapienza, Rome, Italy & Univ. of Tromsø, Norway)
Classical and Bayesian models and methods for Covid-19
Abstract: In this talk, I will present some mathematical models to describe the diffusion of Covid-19 epidemic and some methods for the analysis of related data developed within both classical and Bayesian frameworks. Different aspects will be addressed, e.g. modeling, simulation, estimation, forecast. Some results obtained by applying the mathematical models and methods to Covid-19 data in Italy will be shown.
- Lenka Zdeborová (CEA Saclay), Florent Krzakala and Marc Mézard (ENS Paris), Alfredo Braunstein (Politecnico di Torino) et al
Joint work: A. Baker, I. Biazzo, A. Braunstein, G. Catania, L. Dall Asta, A. Ingrosso, F. Krzakala, F. Mazza, M. Mézard, A. P. Muntoni, M. Refinetti, S. Sarao Mannelli, E. Ortega, L. Zdeborová
Risk estimation from contact tracing data
Abstract: Contact tracing mobile applications are clear candidates enabling us to slow down the epidemics and keep the society running while holding the health risks down. Most of the currently discussed and developed mobile applications aim to notify individuals who were recently in a significant contact with an individual who tested COVID-19 positive. The contacted individuals would then be tested or put in isolation.
In our work, we aim to quantify the epidemiological gain one would obtain if, additionally, individuals who were recently in contact could exchange messages consisting of tens to hundreds of bits per day of information. With such message passing the risk of contracting COVID-19 could be estimated with much better accuracy than simple contact tracing. I will present our preliminary results, with the overall aim to provide quantitative analysis to inform the public discussion about the deployment of contact tracing applications.