Two Multi-Sigmoidal Diffusion Models for the Study of the Evolution of the COVID-19 Pandemic

A proposal is made to employ stochastic models, based on diffusion processes, represent the evolution of SARS-CoV-2 virus pandemic. Specifically, two processes are proposed whose mean functions obey multi-sigmoidal Gompertz and Weibull-type patterns. Both constructed by introducing polynomial in ordinary differential equations that originate classical Weibull curves. The estimation parameters approached maximum likelihood. Various associated problems analyzed, such as determination initial solutions for necessary numerical methods practical cases, well Bayesian determine degree polynomial. Additionally, strategies suggested best model fit specific data. case developed from data originating several Spanish regions during first waves COVID-19 inflection time instants, which correspond peaks infection deaths, given special attention. To deal with this particular issue, point first-passage times have been considered.