Sequential data assimilation of the stochastic SEIR epidemic model for regional COVID-19 dynamics

Engbert, Ralf; Rabe, Maximilian M.; Kliegl, Reinhold; Reich, Sebastian

doi:10.1101/2020.04.13.20063768

Cited by 25 publications

(25 citation statements)

References 24 publications

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“…Since the outbreak of the epidemic, a large number of simulation studies have been conducted using mathematical models to assess the efficacy of different NPIs and to estimate the corresponding demands on the health care system [4][5][6][7][8][9][10][11][12]. Moreover, mathematical models are employed to deduce important epidemiological parameters [13][14][15] and to evaluate the effect of particular measures from empirical data [16,17].…”

Section: Introductionmentioning

confidence: 99%

Beyond just “flattening the curve”: Optimal control of epidemics with purely non-pharmaceutical interventions

2020

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When effective medical treatment and vaccination are not available, non-pharmaceutical interventions such as social distancing, home quarantine and far-reaching shutdown of public life are the only available strategies to prevent the spread of epidemics. Based on an extended SEIR (susceptible-exposed-infectious-recovered) model and continuous-time optimal control theory, we compute the optimal non-pharmaceutical intervention strategy for the case that a vaccine is never found and complete containment (eradication of the epidemic) is impossible. In this case, the optimal control must meet competing requirements: First, the minimization of disease-related deaths, and, second, the establishment of a sufficient degree of natural immunity at the end of the measures, in order to exclude a second wave. Moreover, the socioeconomic costs of the intervention shall be kept at a minimum. The numerically computed optimal control strategy is a single-intervention scenario that goes beyond heuristically motivated interventions and simple "flattening of the curve". Careful analysis of the computed control strategy reveals, however, that the obtained solution is in fact a tightrope walk close to the stability boundary of the system, where socioeconomic costs and the risk of a new outbreak must be constantly balanced against one another. The model system is calibrated to reproduce the initial exponential growth phase of the COVID-19 pandemic in Germany.

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Section: Introductionmentioning

confidence: 99%

Beyond just “flattening the curve”: Optimal control of epidemics with purely non-pharmaceutical interventions

2020

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“…1a). Because of low infection numbers in each region, it is necessary to use a stochastic model with discrete infection events [15] (see Appendix for exact model definition). We assume that the reproduction number R 0 in the overall population in the absence of stringent restrictions is slightly above 1.…”

Section: An Adaptive Local Containment Strategymentioning

confidence: 99%

Local measures enable COVID-19 containment with fewer restrictions due to cooperative effects

Bittihn

Hupe

Isensee

et al. 2020

Preprint

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Many countries worldwide that were successful in containing the first wave of the COVID-19 epidemic are faced with the seemingly impossible choice between the resurgence of infections and endangering the economic and mental well-being of their citizens. While blanket measures are slowly being lifted and infection numbers are monitored, a systematic strategy for balancing contact restrictions and the freedom necessary for a functioning society long-term in the absence of a vaccine is currently lacking. Here, we propose a regional strategy with locally triggered containment measures that can largely circumvent this trade-off and substantially lower the magnitude of restrictions the average individual will have to endure in the near future. For the simulation of future disease dynamics and its control, we use current data on the spread of COVID-19 in Germany, Italy, England, New York State and Florida, taking into account the regional structure of each country and their past lockdown efficiency. Overall, our analysis shows that tight regional control in the short term can lead to long-term net benefits due to small-number effects which are amplified by the regional subdivision and crucially depend on the rate of cross-regional contacts. We outline the mechanisms and parameters responsible for these benefits and suggest possible was to gain access to them, simultaneously achieving more freedom for the population and successfully containing the epidemic. Our open-source simulation code is freely available and can be readily adapted to other countries. We hope that our analysis will help create sustainable, theory-driven long-term strategies for the management of the COVID-19 epidemic until therapy or immunization options are available.

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“…When the computational model arises from a dynamical system, and time dependent observational data of that system are available, then the process of combining the model and the data to obtain a more informed system is called data assimilation. Data assimilation research has been mainly driven by practitioners, initially in the field of numerical weather prediction and ocean modeling [49,50,56,86,87,120,135,139,155,156,164], but nowadays has many more applications in geosciences [38,79,143,171], ecology [130,140], biology [126,151], chemistry [29,66], mechanical engineering [3,47], medicine [68,115], image processing [22,32], as well as human and social sciences [157,159], see also [8] and references therein, with the potential for further utilization in data science and machine learning. In particular, as it becomes easier to make large numbers of relatively accurate observations of a system (we explain later what we mean by a system), a major challenge is how best to use this information to update and refine the model of that system.…”

Section: Motivationmentioning

confidence: 99%

Numerical linear algebra in data assimilation

Freitag

2020

GAMM-Mitteilungen

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Data assimilation is a method that combines observations (ie, real world data) of a state of a system with model output for that system in order to improve the estimate of the state of the system and thereby the model output. The model is usually represented by a discretized partial differential equation. The data assimilation problem can be formulated as a large scale Bayesian inverse problem. Based on this interpretation we will derive the most important variational and sequential data assimilation approaches, in particular three‐dimensional and four‐dimensional variational data assimilation (3D‐Var and 4D‐Var) and the Kalman filter. We will then consider more advanced methods which are extensions of the Kalman filter and variational data assimilation and pay particular attention to their advantages and disadvantages. The data assimilation problem usually results in a very large optimization problem and/or a very large linear system to solve (due to inclusion of time and space dimensions). Therefore, the second part of this article aims to review advances and challenges, in particular from the numerical linear algebra perspective, within the various data assimilation approaches.

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Sequential data assimilation of the stochastic SEIR epidemic model for regional COVID-19 dynamics

Cited by 25 publications

References 24 publications

Beyond just “flattening the curve”: Optimal control of epidemics with purely non-pharmaceutical interventions

Beyond just “flattening the curve”: Optimal control of epidemics with purely non-pharmaceutical interventions

Local measures enable COVID-19 containment with fewer restrictions due to cooperative effects

Numerical linear algebra in data assimilation

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