Information Bottlenecks in Forecasting COVID-19

David Gamarnik, Muzhi Ma


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Reliable short term and long term forecasting of the number of COVID-19 incidences is a task of clear importance. Numerous attempts for such forecasting have been attempted historically since the onset of the pandemic. While many successful short-term forecasting models have been put forward, predictions for mid-range time intervals (few weeks) and long-range ones (few months to half a year) appeared to be largely inaccurate. In this paper we investigate systematically the question as to what extend such predictions are even possible given the information available at the times when the predictions are made. We demonstrate that predictions on the daily basis is practically impossible beyond the horizon of 20+ days, and predictions on the weekly basis is similarly impossible beyond the horizon of roughly half a year. We arrive at this conclusion by computing information bottlenecks arising in the dynamics of the COVID-19 pandemic. Such bottlenecks stem from the “memoryless” property of the stochastic dynamical systems describing COVID-19 evolution, specifically from the so-called mixing rate of the system. The mixing rate is then used to gage the rate at which the information used at a time when predictions are made no longer impacts the actual outcomes of the pandemic. ### Competing Interest Statement The authors have declared no competing interest. ### Funding Statement NSF Grant DMS-2015517 ### Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines, such as any relevant EQUATOR Network research reporting checklist(s) and other pertinent material, if applicable. Yes All data produced in the present study are available upon reasonable request to the authors
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