skip to main content

Title: Data-driven optimized control of the COVID-19 epidemics
Abstract Optimizing the impact on the economy of control strategies aiming at containing the spread of COVID-19 is a critical challenge. We use daily new case counts of COVID-19 patients reported by local health administrations from different Metropolitan Statistical Areas (MSAs) within the US to parametrize a model that well describes the propagation of the disease in each area. We then introduce a time-varying control input that represents the level of social distancing imposed on the population of a given area and solve an optimal control problem with the goal of minimizing the impact of social distancing on the economy in the presence of relevant constraints, such as a desired level of suppression for the epidemics at a terminal time. We find that with the exception of the initial time and of the final time, the optimal control input is well approximated by a constant, specific to each area, which contrasts with the implemented system of reopening ‘in phases’. For all the areas considered, this optimal level corresponds to stricter social distancing than the level estimated from data. Proper selection of the time period for application of the control action optimally is important: depending on the particular MSA this period more » should be either short or long or intermediate. We also consider the case that the transmissibility increases in time (due e.g. to increasingly colder weather), for which we find that the optimal control solution yields progressively stricter measures of social distancing. We finally compute the optimal control solution for a model modified to incorporate the effects of vaccinations on the population and we see that depending on a number of factors, social distancing measures could be optimally reduced during the period over which vaccines are administered to the population. « less
; ;
Award ID(s):
Publication Date:
Journal Name:
Scientific Reports
Sponsoring Org:
National Science Foundation
More Like this
  1. In the past, epidemics such as AIDS, measles, SARS, H1N1 influenza, and tuberculosis caused the death of millions of people around the world. In response, intensive research is evolving to design efficient drugs and vaccines. However, studies warn that new pandemics such as Coronavirus (COVID-19), variants, and even deadly pandemics can emerge in the future. The existing epidemic confinement approaches rely on a large amount of available data to determine policies. Such dependencies could cause an irreversible effect before proper strategies are developed. Furthermore, the existing approaches follow a one-size-fits-all control technique, which might not be effective. To overcome this, in this work, we develop a game-theory-inspired approach that considers societal and economic impacts and formulates epidemic control as a non-zero-sum game. Further, the proposed approach considers the demographic information that provides a tailored solution to each demography. We explore different strategies, including masking, social distancing, contact tracing, quarantining, partial-, and full-lockdowns and their combinations, and present demography-aware optimal solutions to confine a pandemic with minimal history information and optimal impact on the economy. To facilitate scalability, we propose a novel graph learning approach, which learns from the previously obtained COVID-19 game outputs and mobility rates of one state (region)more »depending on the other to produce an optimal solution. Our optimal solution is strategized to restrict the mobility between states based on the impact they are causing on COVID-19 spread. We aim to control the COVID-19 spread by more than 50% and model a dynamic solution that can be applied to different strains of COVID-19. Real-world demographic conditions specific to each state are created, and an optimal strategic solution is obtained to reduce the infection rate in each state by more than 50%.« less
  2. Abstract Hard-to-predict bursts of COVID-19 pandemic revealed significance of statistical modeling which would resolve spatio-temporal correlations over geographical areas, for example spread of the infection over a city with census tract granularity. In this manuscript, we provide algorithmic answers to the following two inter-related public health challenges of immense social impact which have not been adequately addressed (1) Inference Challenge assuming that there are N census blocks (nodes) in the city, and given an initial infection at any set of nodes, e.g. any N of possible single node infections, any $$N(N-1)/2$$ N ( N - 1 ) / 2 of possible two node infections, etc, what is the probability for a subset of census blocks to become infected by the time the spread of the infection burst is stabilized? (2) Prevention Challenge What is the minimal control action one can take to minimize the infected part of the stabilized state footprint? To answer the challenges, we build a Graphical Model of pandemic of the attractive Ising (pair-wise, binary) type, where each node represents a census tract and each edge factor represents the strength of the pairwise interaction between a pair of nodes, e.g. representing the inter-node travel, road closure andmore »related, and each local bias/field represents the community level of immunization, acceptance of the social distance and mask wearing practice, etc. Resolving the Inference Challenge requires finding the Maximum-A-Posteriory (MAP), i.e. most probable, state of the Ising Model constrained to the set of initially infected nodes. (An infected node is in the $$+ \, 1$$ + 1 state and a node which remained safe is in the $$- \, 1$$ - 1 state.) We show that almost all attractive Ising Models on dense graphs result in either of the two possibilities (modes) for the MAP state: either all nodes which were not infected initially became infected, or all the initially uninfected nodes remain uninfected (susceptible). This bi-modal solution of the Inference Challenge allows us to re-state the Prevention Challenge as the following tractable convex programming : for the bare Ising Model with pair-wise and bias factors representing the system without prevention measures, such that the MAP state is fully infected for at least one of the initial infection patterns, find the closest, for example in $$l_1$$ l 1 , $$l_2$$ l 2 or any other convexity-preserving norm, therefore prevention-optimal, set of factors resulting in all the MAP states of the Ising model, with the optimal prevention measures applied, to become safe. We have illustrated efficiency of the scheme on a quasi-realistic model of Seattle. Our experiments have also revealed useful features, such as sparsity of the prevention solution in the case of the $$l_1$$ l 1 norm, and also somehow unexpected features, such as localization of the sparse prevention solution at pair-wise links which are NOT these which are most utilized/traveled.« less
  3. null (Ed.)
    Understanding the dynamics of the spread of COVID-19 between connected communities is fundamental in planning appropriate mitigation measures. To that end, we propose and analyze a novel metapopulation network model, particularly suitable for modeling commuter traffic patterns, that takes into account the connectivity between a heterogeneous set of communities, each with its own infection dynamics. In the novel metapopulation model that we propose here, transport schemes developed in optimal transport theory provide an efficient and easily implementable way of describing the temporary population redistribution due to traffic, such as the daily commuter traffic between work and residence. Locally, infection dynamics in individual communities are described in terms of a susceptible-exposed-infected-recovered (SEIR) compartment model, modified to account for the specific features of COVID-19, most notably its spread by asymptomatic and presymptomatic infected individuals. The mathematical foundation of our metapopulation network model is akin to a transport scheme between two population distributions, namely the residential distribution and the workplace distribution, whose interface can be inferred from commuter mobility data made available by the US Census Bureau. We use the proposed metapopulation model to test the dynamics of the spread of COVID-19 on two networks, a smaller one comprising 7 counties in themore »Greater Cleveland area in Ohio, and a larger one consisting of 74 counties in the Pittsburgh–Cleveland–Detroit corridor following the Lake Erie’s American coastline. The model simulations indicate that densely populated regions effectively act as amplifiers of the infection for the surrounding, less densely populated areas, in agreement with the pattern of infections observed in the course of the COVID-19 pandemic. Computed examples show that the model can be used also to test different mitigation strategies, including one based on state-level travel restrictions, another on county level triggered social distancing, as well as a combination of the two.« less
  4. Abstract Background

    No versatile web app exists that allows epidemiologists and managers around the world to comprehensively analyze the impacts of COVID-19 mitigation. The app presented here fills this gap.


    Our web app uses a model that explicitly identifies susceptible, contact, latent, asymptomatic, symptomatic and recovered classes of individuals, and a parallel set of response classes, subject to lower pathogen-contact rates. The user inputs a CSV file of incidence and, if of interest, mortality rate data. A default set of parameters is available that can be overwritten through input or online entry, and a user-selected subset of these can be fitted to the model using maximum-likelihood estimation (MLE). Model fitting and forecasting intervals are specifiable and changes to parameters allow counterfactual and forecasting scenarios. Confidence or credible intervals can be generated using stochastic simulations, based on MLE values, or on an inputted CSV file containing Markov chain Monte Carlo (MCMC) estimates of one or more parameters.


    We illustrate the use of our web app in extracting social distancing, social relaxation, surveillance or virulence switching functions (i.e., time varying drivers) from the incidence and mortality rates of COVID-19 epidemics in Israel, South Africa, and England. The Israeli outbreak exhibits fourmore »distinct phases: initial outbreak, social distancing, social relaxation, and a second wave mitigation phase. An MCMC projection of this latter phase suggests the Israeli epidemic will continue to produce into late November an average of around 1500 new case per day, unless the population practices social-relaxation measures at least 5-fold below the level in August, which itself is 4-fold below the level at the start of July. Our analysis of the relatively late South African outbreak that became the world’s fifth largest COVID-19 epidemic in July revealed that the decline through late July and early August was characterised by a social distancing driver operating at more than twice the per-capita applicable-disease-class (pc-adc) rate of the social relaxation driver. Our analysis of the relatively early English outbreak, identified a more than 2-fold improvement in surveillance over the course of the epidemic. It also identified a pc-adc social distancing rate in early August that, though nearly four times the pc-adc social relaxation rate, appeared to barely contain a second wave that would break out if social distancing was further relaxed.


    Our web app provides policy makers and health officers who have no epidemiological modelling or computer coding expertise with an invaluable tool for assessing the impacts of different outbreak mitigation policies and measures. This includes an ability to generate an epidemic-suppression or curve-flattening index that measures the intensity with which behavioural responses suppress or flatten the epidemic curve in the region under consideration.

    « less
  5. In the last decades, emerging and re-emerging epidemics such as AIDS, measles, SARS, HINI influenza, and tuberculosis cause death to millions of people each year. In response, a large and intensive research is evolving for the design of better drugs and vaccines. However, studies warn that the new pandemics such as Coronavirus (COVID-19) and even deadly pandemics can emerge in the future. The existing confinement approaches rely on large amount of available data to determine policies. Such dependencies could cause an irreversible effect before proper strategies are developed. Furthermore, the existing approaches follow a one-size fits all approach, which might not be effective. In contrast, we develop a game-theory inspired approach that considers societal and economic impacts and formulates the epidemic control as a non-zero sum dynamic game. Further, the proposed approach considers the demographic information leading to providing a tailored solution to each demography. We explore different strategies including masking, social distancing, contact tracing, quarantining, partial-, and full-lockdowns and their combinations and present demography-aware optimal solutions to confine a pandemic with minimal history information and optimal impact on economy.