The remission point of an epidemic identified by elasticity. Application to the first wave of COVID-19 in Chile

Abstract

Introduction. Detecting changes in the evolution of a random process, known as the problem of change, has become a quickly developing area of statistical research. The correct and rapid detection of changes is relevant in many real-life situations, particularly in epidemiology.
Materials and Methods. As a new metric to time-locate the moment of remission of an epidemic (moment of change), the concept of the elasticity of a probability distribution is applied to the recent COVID-19 pandemic in Chile.
Results. The application shows that there is a delay between the “peak” day, or day with the highest number of cases, and the “remission” day as identified by elasticity. In this period, between peak and remission, the epidemic control measures should not be relaxed. A di¬fference of 20 days is obtained between the remission points of the series of infections and deaths. This figure can be interpreted as an estimate of survival time for those diagnosed with the disease who subsequently died during the first wave of COVID-19. Comparing the results of the application with that of other South American countries, we observe the same result as that attained for Chile, although with significantly longer delay times between the peak and the point of remission.
Discussion. The measure used in this study is easy to communicate, does not require the prior formulation of hypotheses about the behaviour of the data and can be applied in real time, as and when the data is known. These characteristics of easy applicability and interpretation, generating reasonable results, make the application convenient for the study of change in epidemiological series.