Philip Bittihn, Lukas Hupe, Jonas Isensee, Ramin Golestanian (2021)
Abstract: 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.
Jonas Isensee, George Datseris, Ulrich Parlitz (2019)
Abstract: We present a method for both cross-estimation and iterated time series prediction of spatio-temporal dynamics based on local modelling and dimension reduction techniques. Assuming homogeneity of the underlying dynamics, we construct delay coordinates of local states and then further reduce their dimensionality through Principle Component Analysis. The prediction uses nearest neighbour methods in the space of dimension reduced states to either cross-estimate or iteratively predict the future of a given frame. The effectiveness of this approach is shown for (noisy) data from a (cubic) Barkley model, the Bueno-Orovio-Cherry-Fenton model, and the Kuramoto-Sivashinsky model.