On interval prediction of COVID-19 development in France based on a SEIR epidemic model
14 Dec 2020-pp 3883-3888
TL;DR: In this paper, the authors identify the parameters of an original modified SEIR model for the COVID-19 epidemic's course in France by using publicly available data and apply such an identified model to the prediction of the SARS-CoV-2 virus propagation under different conditions of confinement.
Abstract: This paper aims to identify the parameters of an original modified SEIR model for the COVID-19 epidemic’s course in France by using publicly available data and applying such an identified model for the prediction of the SARS-CoV-2 virus propagation under different conditions of confinement. For this purpose, an interval predictor is designed, allowing variations and uncertainties in the model parameters to be taken into account.
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TL;DR: A new version of the well-known epidemic mathematical SEIR model is used to analyze the pandemic course of COVID-19 in eight different countries, and one of the proposed model’s improvements is to reflect the societal feedback on the disease and confinement features.
52 citations
TL;DR: In this paper, a mathematical framework for the in-homogeneous spatial spreading of an infectious disease in human population, with particular attention to COVID-19, is proposed, which includes five different sub-populations, in which the infectious sub-population is split into pre-symptomatic and symptomatic.
Abstract: We suggest a novel mathematical framework for the in-homogeneous spatial spreading of an infectious disease in human population, with particular attention to COVID-19. Common epidemiological models, e.g., the well-known susceptible-exposed-infectious-recovered (SEIR) model, implicitly assume uniform (random) encounters between the infectious and susceptible sub-populations, resulting in homogeneous spatial distributions. However, in human population, especially under different levels of mobility restrictions, this assumption is likely to fail. Splitting the geographic region under study into areal nodes, and assuming infection kinetics within nodes and between nearest-neighbor nodes, we arrive into a continuous, "reaction-diffusion", spatial model. To account for COVID-19, the model includes five different sub-populations, in which the infectious sub-population is split into pre-symptomatic and symptomatic. Our model accounts for the spreading evolution of infectious population domains from initial epicenters, leading to different regimes of sub-exponential (e.g., power-law) growth. Importantly, we also account for the variable geographic density of the population, that can strongly enhance or suppress infection spreading. For instance, we show how weakly infected regions surrounding a densely populated area can cause rapid migration of the infection towards the populated area. Predicted infection "heat-maps" show remarkable similarity to publicly available heat-maps, e.g., from South Carolina. We further demonstrate how localized lockdown/quarantine conditions can slow down the spreading of disease from epicenters. Application of our model in different countries can provide a useful predictive tool for the authorities, in particular, for planning strong lockdown measures in localized areas-such as those underway in a few countries.
15 citations
TL;DR: In this article, the authors use a model-based approach based on a stochastic susceptible-infections-removed (SIR) model with time-varying parameters, which captures the evolution of the disease dynamics in response to changes in social behavior, non-pharmaceutical interventions, and testing rates.
13 citations
TL;DR: In this article, an extended SEIR model and daily data of COVID-19 cases in the U.S. and the seven largest European countries were used to forecast possible pandemic dynamics by investigating the effects of infection vulnerability stratification and measures on preventing the spread of infection.
Abstract: Basic Susceptible-Exposed-Infectious-Removed (SEIR) models of COVID-19 dynamics tend to be excessively pessimistic due to high basic reproduction values, which result in overestimations of cases of infection and death. We propose an extended SEIR model and daily data of COVID-19 cases in the U.S. and the seven largest European countries to forecast possible pandemic dynamics by investigating the effects of infection vulnerability stratification and measures on preventing the spread of infection. We assume that (i) the number of cases would be underestimated at the beginning of a new virus pandemic due to the lack of effective diagnostic methods and (ii) people more susceptible to infection are more likely to become infected; whereas during the later stages, the chances of infection among others will be reduced, thereby potentially leading to pandemic cessation. Based on infection vulnerability stratification, we demonstrate effects brought by the fraction of infected persons in the population at the start of pandemic deceleration on the cumulative fraction of the infected population. We interestingly show that moderate and long-lasting preventive measures are more effective than more rigid measures, which tend to be eventually loosened or abandoned due to economic losses, delay the peak of infection and fail to reduce the total number of cases. Our calculations relate the pandemic's second wave to high seasonal fluctuations and a low vulnerability stratification coefficient. Our characterisation of basic reproduction dynamics indicates that second wave of the pandemic is likely to first occur in Germany, Spain, France, and Italy, and a second wave is also possible in the U.K. and the U.S. Our findings show that even if the total elimination of the virus is impossible, the total number of infected people can be reduced during the deceleration stage.
13 citations
TL;DR: This work develops a continuous spatial model that includes five different populations, in which the infectious population is split into latent (or pre-symptomatic) and symptomatic, and arrives into a ``reaction-diffusion'' model, which demonstrates how infected domains spread outward from epicenters/hotspots, leading to different regimes of sub-exponential growth.
Abstract: We suggest a mathematical model for the spread of an infectious disease in human population, with particular attention to the COVID-19. Common epidemiological models, e.g., the well-known susceptible-exposed-infectious-recovered (SEIR) model, implicitly assume fast mixing of the population relative to the local infection rate, similar to the regime applicable to many chemical reactions. However, in human populations, especially under different levels of quarantine conditions, this assumption is likely to fail. We develop a continuous spatial model that includes five different populations, in which the infectious population is split into latent (or pre-symptomatic) and symptomatic. Based on nearest-neighbor infection kinetics, we arrive into a “reaction-diffusion” model. Our model accounts for front propagation of the infectious population domains under partial quarantine conditions, which is present on top of the common local infection process. Importantly, we also account for the variable geographic density of the population, that can strongly enhance or suppress infection spreading. Our results demonstrate how infected domains spread outward from epicenters/hotspots, leading to different regimes of sub-exponential (quasi linear or power-law) growth. Moreover, we show how weakly infected regions surrounding a densely populated area can cause rapid migration of the infection towards the center of the populated area. Predicted heat-maps show remarkable similarity to recently media released heat-maps. We further demonstrate how localized strong quarantine conditions can prevent the spreading of the disease from an epicenter/hotspot, significantly reducing the number of infected people. Application of our model in different countries, using actual demographic data and infectious disease parameters, can provide a useful predictive tool for the authorities, in particular, for planning strong lockdown measures in localized areas.
10 citations
References
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TL;DR: The results support current proposals for the length of quarantine or active monitoring of persons potentially exposed to SARS-CoV-2, although longer monitoring periods might be justified in extreme cases.
Abstract: Using news reports and press releases from provinces, regions, and countries outside Wuhan, Hubei province, China, this analysis estimates the length of the incubation period of COVID-19 and its pu...
5,215 citations
Book•
28 Oct 2007TL;DR: Mathematical modeling of infectious dis-eases has progressed dramatically over the past 3 decades and continues to be a valuable tool at the nexus of mathematics, epidemiol-ogy, and infectious diseases research.
Abstract: By Matthew James Keelingand Pejman RohaniPrinceton, NJ: Princeton University Press,2008.408 pp., Illustrated. $65.00 (hardcover).Mathematical modeling of infectious dis-eases has progressed dramatically over thepast 3 decades and continues to flourishat the nexus of mathematics, epidemiol-ogy, and infectious diseases research. Nowrecognized as a valuable tool, mathemat-ical models are being integrated into thepublic health decision-making processmore than ever before. However, despiterapid advancements in this area, a formaltraining program for mathematical mod-eling is lacking, and there are very fewbooks suitable for a broad readership. Tosupport this bridging science, a commonlanguage that is understood in all con-tributing disciplines is required.
3,467 citations
DOI•
16 Mar 2020
TL;DR: Neil M Ferguson, Daniel Laydon, Gemma Nedjati-Gilani, Natsuko Imai, Kylie Ainslie, Sangeeta Bhatia, Adhiratha Boonyasiri, Zulma Cucunubá, Gina Cuomo-Dannenburg, Amy Dighe, Ilaria Dorigatti, Han Fu, Katy Gaythorpe, Will Green, Arran Hamlet, Wes Hinsley, Lucy C Okell.
Abstract: The global impact of COVID-19 has been profound, and the public health threat it represents is the most serious seen in a respiratory virus since the 1918 H1N1 influenza pandemic. Here we present the results of epidemiological modelling which has informed policymaking in the UK and other countries in recent weeks. In the absence of a COVID-19 vaccine, we assess the potential role of a number of public health measures – so-called non-pharmaceutical interventions (NPIs) – aimed at reducing contact rates in the population and thereby reducing transmission of the virus. In the results presented here, we apply a previously published microsimulation model to two countries: the UK (Great Britain specifically) and the US. We conclude that the effectiveness of any one intervention in isolation is likely to be limited, requiring multiple interventions to be combined to have a substantial impact on transmission. Two fundamental strategies are possible: (a) mitigation, which focuses on slowing but not necessarily stopping epidemic spread – reducing peak healthcare demand while protecting those most at risk of severe disease from infection, and (b) suppression, which aims to reverse epidemic growth, reducing case numbers to low levels and maintaining that situation indefinitely. Each policy has major challenges. We find that that optimal mitigation policies (combining home isolation of suspect cases, home quarantine of those living in the same household as suspect cases, and social distancing of the elderly and others at most risk of severe disease) might reduce peak healthcare demand by 2/3 and deaths by half. However, the resulting mitigated epidemic would still likely result in hundreds of thousands of deaths and health systems (most notably intensive care units) being overwhelmed many times over. For countries able to achieve it, this leaves suppression as the preferred policy option. We show that in the UK and US context, suppression will minimally require a combination of social distancing of the entire population, home isolation of cases and household quarantine of their family members. This may need to be supplemented by school and university closures, though it should be recognised that such closures may have negative impacts on health systems due to increased absenteeism. The major challenge of suppression is that this type of intensive intervention package – or something equivalently effective at reducing transmission – will need to be maintained until a vaccine becomes available (potentially 18 months or more) – given that we predict that transmission will quickly rebound if interventions are relaxed. We show that intermittent social distancing – triggered by trends in disease surveillance – may allow interventions to be relaxed temporarily in relative short time windows, but measures will need to be reintroduced if or when case numbers rebound. Last, while experience in China and now South Korea show that suppression is possible in the short term, it remains to be seen whether it is possible long-term, and whether the social and economic costs of the interventions adopted thus far can be reduced.
2,908 citations
TL;DR: The implementation of control measures on January 23 2020 was indispensable in reducing the eventual COVID-19 epidemic size, and the dynamic SEIR model, trained on the 2003 SARS data, was effective in predicting the epidemic peaks and sizes.
Abstract: Background: The coronavirus disease 2019 (COVID-19) outbreak originating in Wuhan, Hubei province, China, coincided with chunyun, the period of mass migration for the annual Spring Festival. To contain its spread, China adopted unprecedented nationwide interventions on January 23 2020. These policies included large-scale quarantine, strict controls on travel and extensive monitoring of suspected cases. However, it is unknown whether these policies have had an impact on the epidemic. We sought to show how these control measures impacted the containment of the epidemic.
Methods: We integrated population migration data before and after January 23 and most updated COVID-19 epidemiological data into the Susceptible-Exposed-Infectious-Removed (SEIR) model to derive the epidemic curve. We also used an artificial intelligence (AI) approach, trained on the 2003 SARS data, to predict the epidemic.
Results: We found that the epidemic of China should peak by late February, showing gradual decline by end of April. A five-day delay in implementation would have increased epidemic size in mainland China three-fold. Lifting the Hubei quarantine would lead to a second epidemic peak in Hubei province in mid-March and extend the epidemic to late April, a result corroborated by the machine learning prediction.
Conclusions: Our dynamic SEIR model was effective in predicting the COVID-19 epidemic peaks and sizes. The implementation of control measures on January 23 2020 was indispensable in reducing the eventual COVID-19 epidemic size.
1,172 citations
TL;DR: This report reviews the developmental arc of theoretical epidemiology with emphasis on vaccination, as it led from classical models assuming homogeneously mixing populations and ignoring human behavior, to recent models that account for behavioral feedback and/or population spatial/social structure.
789 citations