COVID-19's pandemic: a new way of thinking through linear combinations of proportions

Knowledge about the evolution of an epidemic is of critical importance for assessing the needs of the National Health System (NHS), planning the necessary responses and coordinating resources countrywide. In this work, we analyze the behavior of the COVID-19 epidemic curve in Portugal, by using linear combinations of proportions. These proportions are based on the number of nonhospitalized and hospitalized cases and deaths. The trajectories of different linear relations of proportions and pairs of two proportions are graphically displayed in order to allow the comparison of their behaviors over time. By using as the baseline the summer period of 2020, which corresponds to the “lowest level” of the epidemic curve and is what we consider a “comfortable” scenario for the NHS, we identified several linear relations of proportions that may be used to highlight relevant transitions between future periods of the epidemic and thus provide indicators for assessing the overall state of the resources of the NHS dedicated to treating COVID-19 patients. Our analysis shows an association between the implementation of public health measures and the easing of the pressure over the NHS. These indicators can potentially be used to better prevent the exhaustion of the NHS resources.