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The rapid spread of the Coronavirus (COVID-19) confronts policy makers with the problem of measuring the effectiveness of containment strategies, balancing public health considerations with the economic costs of social distancing measures. We introduce a modified epidemic model that we name the controlled-SIR model, in which the disease reproduction rate evolves dynamically in response to political and societal reactions. An analytic solution is presented. The model reproduces official COVID-19 cases counts of a large number of regions and countries that surpassed the first peak of the outbreak. A single unbiased feedback parameter is extracted from field data and used to formulate an index that measures the efficiency of containment strategies (the CEI index). CEI values for a range of countries are given. For two variants of the controlled-SIR model, detailed estimates of the total medical and socio-economic costs are evaluated over the entire course of the epidemic. Costs comprise medical care cost, the economic cost of social distancing, as well as the economic value of lives saved. Under plausible parameters, strict measures fare better than a hands-off policy. Strategies based on current case numbers lead to substantially higher total costs than strategies based on the overall history of the epidemic.
Predicting the cumulative medical load of COVID-19 outbreaks after the peak in daily fatalities
(2021)
The distinct ways the COVID-19 pandemic has been unfolding in different countries and regions suggest that local societal and governmental structures play an important role not only for the baseline infection rate, but also for short and long-term reactions to the outbreak. We propose to investigate the question of how societies as a whole, and governments in particular, modulate the dynamics of a novel epidemic using a generalization of the SIR model, the reactive SIR (short-term and long-term reaction) model. We posit that containment measures are equivalent to a feedback between the status of the outbreak and the reproduction factor. Short-term reaction to an outbreak corresponds in this framework to the reaction of governments and individuals to daily cases and fatalities. The reaction to the cumulative number of cases or deaths, and not to daily numbers, is captured in contrast by long-term reaction. We present the exact phase space solution of the controlled SIR model and use it to quantify containment policies for a large number of countries in terms of short and long-term control parameters. We find increased contributions of long-term control for countries and regions in which the outbreak was suppressed substantially together with a strong correlation between the strength of societal and governmental policies and the time needed to contain COVID-19 outbreaks. Furthermore, for numerous countries and regions we identified a predictive relation between the number of fatalities within a fixed period before and after the peak of daily fatality counts, which allows to gauge the cumulative medical load of COVID-19 outbreaks that should be expected after the peak. These results suggest that the proposed model is applicable not only for understanding the outbreak dynamics, but also for predicting future cases and fatalities once the effectiveness of outbreak suppression policies is established with sufficient certainty. Finally, we provide a web app (https://itp.uni-frankfurt.de/covid-19/) with tools for visualising the phase space representation of real-world COVID-19 data and for exporting the preprocessed data for further analysis.
The phase diagram of the square lattice bilayer Hubbard model: a variational Monte Carlo study
(2014)
We investigate the phase diagram of the square lattice bilayer Hubbard model at half-filling with the variational Monte Carlo method for both the magnetic and the paramagnetic case as a function of the interlayer hopping and on-site Coulomb repulsion U. With this study we resolve some discrepancies in previous calculations based on the dynamical mean-field theory, and we are able to determine the nature of the phase transitions between metal, Mott insulator and band insulator. In the magnetic case we find only two phases: an antiferromagnetic Mott insulator at small for any value of U and a band insulator at large . At large U values we approach the Heisenberg limit. The paramagnetic phase diagram shows at small a metal to Mott insulator transition at moderate U values and a Mott to band insulator transition at larger U values. We also observe a re-entrant Mott insulator to metal transition and metal to band insulator transition for increasing in the range of . Finally, we discuss the phase diagrams obtained in relation to findings from previous studies based on different many-body approaches.