This paper focuses on an important issue of disease progression of COVID-19 (coronavirus disease 2019) through processing COVID-19 cough sounds by proposing a fully-automated method. The new method is based on time-domain exploiting only phase 1 data which is always available for any cough events. The proposed approach generates plausible click sequences consist of clicks for various cough samples from covid-19 patients. The click sequence, which is extracted from the phase slope function of an input signal, is used to calculate inter-click intervals (ICIs), and thereby a scoring index (SI) is derived based on coefficient of variation(CV) of the extracted ICIs. Moreover, probability density function (pdf) of the output click sequence is obtained. The method does not need to adjust any parameters. The experimental results achieved from real-recorded COVID-19 cough data using the medically annotated Novel Coronavirus Cough Database (NoCoCoDa) reveal that the proposed time-domain method can be a very useful tool for automatic cough sound processing to determine the disease progression of coronavirus patients.