Mathematical modelling of COVID-19 with periodic transmission: The case of South Africa

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Abstract The data on SARS-CoV-2 (COVID-19) in South Africa shows seasonal transmission patterns to date, with the peaks having occurred in winter and summer since the out-breaks began. The transmission dynamics have mainly been driven by variations in environmental factors and virus evolution, and the two are at the center of driving the different waves of the disease. It is thus important to understand the role of seasonality in the transmission dynamics of COVID-19. In this paper a compartmental model with a time dependent transmission rate is formulated and the stabilities of the steady states analysed. We note that if R 0 < 1, the disease-free equilibrium is globally asymptotically stable, and the disease completely dies out and when R 0 > 1, the system admits a positive periodic solution, and the disease is uniformly or periodically persistent. The model is fitted to data on new cases in South Africa for the first four waves. The model results clearly indicate the need to consider seasonality in the transmission dynamics of COVID-19 and its importance in modelling fluctuations in the data for new cases. The potential impact of seasonality in the transmission patterns of COVID-19 and the public health implications are discussed.

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