Development of the Gamma Diffusion Process Modified and Applications
Diffusion processes. Covid-19. Effective Reproductive Number. Predictive ability
The covid-19 pandemic is the biggest health emergency since the Spanish flu at the
beginning of the last century. The extent to which these and other diseases spread in the population is determined by the Effective Reproductive Number (Re). The objective of this research is to verify the suitability of the Modified Conditional Gamma model to describe the Re dynamics of covid-19. Therefore, it is shown that the temporal evolution of Re can be mathematically characterized as a diffusive stochastic process. The database used concerns cases of covid-19 in Brazil between the years 2020 and 2022, obtained from the Brazilian online platform OpenDataSUS, with the “Date of First Symptoms” being the primary data for all analyzes in this research. Data are treated and analyzed according to parameters indicated by the Pan American Health Organization (PAHO). When applying the model to the data, the behavior of the parameters ξ and λ is verified for different scenarios and periods. Then, the predictive ability of the model is tested using envelope plots. The indication of a good predictive capacity of the model under analysis is the central point of the research, since it provides useful information to those responsible for decision-making. Finally, some improvements are indicated in the Modified Conditional Gamma model and possibilities for research extension in partnership with health researchers.