Estimation and prediction of the multiply exponentially decaying daily case fatality rate of COVID-19.

The spread of the COVID-19 disease has had significant social and economic impacts all over the world. Numerous measures such as school closures, social distancing, and travel restrictions were implemented during the COVID-19 pandemic outbreak. Currently, as we move into the post-COVID-19 world, we must be prepared for another pandemic outbreak in the future. Having experienced the COVID-19 pandemic, it is imperative to ascertain the conclusion of the pandemic to return to normalcy and plan for the future. One of the beneficial features for deciding the termination of the pandemic disease is the small value of the case fatality rate (CFR) of coronavirus disease 2019 (COVID-19). There is a tendency of gradually decreasing CFR after several increases in CFR during the COVID-19 pandemic outbreak. However, it is difficult to capture the time-dependent CFR of a pandemic outbreak using a single exponential coefficient because it contains multiple exponential decays, i.e., fast and slow decays. Therefore, in this study, we develop a mathematical model for estimating and predicting the multiply exponentially decaying CFRs of the COVID-19 pandemic in different nations: the Republic of Korea, the USA, Japan, and the UK. We perform numerical experiments to validate the proposed method with COVID-19 data from the above-mentioned four nations.

An Explicit Adaptive Finite Difference Method for the Cahn-Hilliard Equation.

In this study, we propose an explicit adaptive finite difference method (FDM) for the Cahn-Hilliard (CH) equation which describes the process of phase separation. The CH equation has been successfully utilized to model and simulate diverse field applications such as complex interfacial fluid flows and materials science. To numerically solve the CH equation fast and efficiently, we use the FDM and time-adaptive narrow-band domain. For the adaptive grid, we define a narrow-band domain including the interfacial transition layer of the phase field based on an undivided finite difference and solve the numerical scheme on the narrow-band domain. The proposed numerical scheme is based on an alternating direction explicit (ADE) method. To make the scheme conservative, we apply a mass correction algorithm after each temporal iteration step. To demonstrate the superior performance of the proposed adaptive FDM for the CH equation, we present two- and three-dimensional numerical experiments and compare them with those of other previous methods.