Some topics in modelling South African COVID-19 epidemiological data.
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Date
2023
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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.
Description
Masters Degree. University of KwaZulu-Natal, Durban.