Some topics in modelling South African COVID-19 epidemiological data.

Abstract

The ongoing COVID-19 epidemic produces a wide variety of quality data, which can be analyzed using simple mathematical models inspired by statistical physics. We explore some underlying methods and apply them to the simulated data using parameters extracted from the previously analyzed data by Pulliam et al. to determine whether the Omicron variant reinfects at a higher rate compared to other previous Variants of Concern. First, using simple prototype models, we investigate whether simple dynamical systems of low dimensions are inherently predictable. The concept of a strange attractor is defined and numerically explored using the Duffing oscillator as an example. The statistical theory of linear parametric models is then investigated mathematically and applied to some standard datasets with the R statistical programming language. We also study the Markov Chain Monte Carlo technique, exploring complicated models and presenting mathematical theory, numerical implementation, optimization, and convergence diagnostics. Finally, we apply the MCMC techniques to estimate the parameters of our model using simulated data for reinfections. Based on the analysis of the mock data, we found that the Omicron variant does not have a higher reinfection rate, as expected since our simulated data for reinfections had no difference in the reinfection rate. Although Pulliam et al. claimed to make all their data available, the required data for analyzing relative reinfection rates was not made publicly available, supposedly on account of privacy concerns. This is why we were forced to use mock data, which in any case would need to be generated to test and validate the code.