Abstract
The COVID-19 pandemic resulted in approximately 800 million infections globally and led
to the deaths of around 7 million individuals. As a contribution to understanding this disease
further, this study focuses on modelling Covid-19 vaccine hesitancy in South Africa using a
calibration protocol for parameter estimation. Initially, we develop a mathematical model for
Covid-19 that incorporates vaccination and vaccine hesitancy. The model is analysed using
mathematical principles to assess the positivity and boundness of solutions as well as existence
and stability of equilibrium points. A calibration procedure is developed in R software
to estimate the model’s parameters from an initial set drawn from literature. The optimised
parameters are then used to project various scenarios based on high and low levels of vaccine
hesitancy, vaccination rate and vaccine efficacy in the population. The worst case scenario,
which resulted in the highest number of infections, was when there was low vaccination rate,
low vaccine efficacy and high vaccine hesitancy. However, the study also shows that low vaccine
hesitancy and high vaccine efficacy are crucial for controlling the spread of Covid-19. In
conclusion, we recommend the use of the calibration protocol in settings where the time and
computational resources are constrained. On vaccine hesitancy, we conclude that governments,
in countries prone to vaccine apathy, should consider setting up a National Vaccine Communication
Task Force, to spearhead all vaccination information dissemination.
Key words: Mathematical model, Calibration Protocol, Covid-19, vaccine hesitancy