The Quixotic Task of Forecasting Peaks of COVID-19: Rather Focus on Forward and Backward Projections.

Over the last months, mathematical models have been extensively used to help control the COVID-19 pandemic worldwide. Although extremely useful in many tasks, most models have performed poorly in forecasting the pandemic peaks. We investigate this common pitfall by forecasting four countries' pandemic peak: Austria, Germany, Italy, and South Korea. Far from the peaks, our models can forecast the pandemic dynamics 20 days ahead. Nevertheless, when calibrating our models close to the day of the pandemic peak, all forecasts fail. Uncertainty quantification and sensitivity analysis revealed the main obstacle: the misestimation of the transmission rate. Inverse uncertainty quantification has shown that significant changes in transmission rate commonly precede a peak. These changes are a key factor in forecasting the pandemic peak. Long forecasts of the pandemic peak are therefore undermined by the lack of models that can forecast changes in the transmission rate, i.e., how a particular society behaves, changes of mitigation policies, or how society chooses to respond to them. In addition, our studies revealed that even short forecasts of the pandemic peak are challenging. Backward projections have shown us that the correct estimation of any temporal change in the transmission rate is only possible many days ahead. Our results suggest that the distance between a change in the transmission rate and its correct identification in the curve of active infected cases can be as long as 15 days. This is intrinsic to the phenomenon and how it affects epidemic data: a new case is usually only reported after an incubation period followed by a delay associated with the test. In summary, our results suggest the phenomenon itself challenges the task of forecasting the peak of the COVID-19 pandemic when only epidemic data is available. Nevertheless, we show that exciting results can be obtained when using the same models to project different scenarios of reduced transmission rates. Therefore, our results highlight that mathematical modeling can help control COVID-19 pandemic by backward projections that characterize the phenomena' essential features and forward projections when different scenarios and strategies can be tested and used for decision-making.

Characterization of the COVID-19 pandemic and the impact of uncertainties, mitigation strategies, and underreporting of cases in South Korea, Italy, and Brazil.

By April 7th, 2020, the Coronavirus disease 2019 (COVID-19) has infected one and a half million people worldwide, accounting for over 80 thousand of deaths in 209 countries and territories around the world. The new and fast dynamics of the pandemic are challenging the health systems of different countries. In the absence of vaccines or effective treatments, mitigation policies, such as social isolation and lock-down of cities, have been adopted, but the results vary among different countries. Some countries were able to control the disease at the moment, as is the case of South Korea. Others, like Italy, are now experiencing the peak of the pandemic. Finally, countries with emerging economies and social issues, like Brazil, are in the initial phase of the pandemic. In this work, we use mathematical models with time-dependent coefficients, techniques of inverse and forward uncertainty quantification, and sensitivity analysis to characterize essential aspects of the COVID-19 in the three countries mentioned above. The model parameters estimated for South Korea revealed effective social distancing and isolation policies, border control, and a high number in the percentage of reported cases. In contrast, underreporting of cases was estimated to be very high in Brazil and Italy. In addition, the model estimated a poor isolation policy at the moment in Brazil, with a reduction of contact around 40%, whereas Italy and South Korea estimated numbers for contact reduction are at 75% and 90%, respectively. This characterization of the COVID-19, in these different countries under different scenarios and phases of the pandemic, supports the importance of mitigation policies, such as social distancing. In addition, it raises serious concerns for socially and economically fragile countries, where underreporting poses additional challenges to the management of the COVID-19 pandemic by significantly increasing the uncertainties regarding its dynamics.

Uniformization method for solving cardiac electrophysiology models based on the Markov-chain formulation.

This paper compares different numerical methods for the solution of myocyte models of cardiac electrophysiology. In particular, it presents how the technique called uniformization method substantially increases the stability of simple first-order methods such as Euler explicit method and Rush-Larsen (RL) method, for the solution of modern electrophysiology models that are based on continuous-time Markov chains (MCs) for the description of subcellular structures, such as ion channels. The MCs are often associated with stiff ordinary differential equations that severely limit the time step used by these traditional methods. By using the uniformization method, we could significantly increase the time steps for the solution of different cardiac electrophysiology models and improve the computational performance up to 150 times compared to the performance of Euler's and RL's methods.