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In a recent paper we established the Extended Gompertz Function Model as a phenomenological model for Covid-19, in which the cumulative ‘events’ (cases, hospitalizations, ICU admissions, deaths) follows alternating phases of Gompertz Function growth and piecewise-linear growth.

This model has excellent predictive power out of sample, using non-linear regression fits of Gompertz Functions to epidemic data, for short to medium term forecasts. First for a few days and then for weeks at a time with increasing accuracy.

This is a purely data driven method to navigate through successive waves of Covid-19. The forecasting problem is reduced to identifying the transitions from linear growth to Gompertz Function growth and providing reliable bounds on growth in the initial Gompertz Function phase where its predictive power is lowest.

We illustrate with examples from England and Ontario, describe the origins of this model in Portuguese influenza data and indicate the connection to geometry and differential invariants that makes Gompertz Functions effectively inevitable in models that accurately model epidemic data.

Ana Cascon and William F. Shadwick have decades of experience in industry and academia. They are the founders of Omega Analysis (OmegaAnalysis.com) where prize winning technology is based on their fundamental mathematical discoveries in probability and statistics. They are currently on an extended visit to IMPA, Brazil’s national mathematics research institute in Rio de Janeiro.

Related publication: 'Predicting the course of Covid-19 and other epidemic and endemic disease' https://www.medrxiv.org/content/10.1101/2021.12.26.21268419v1