Mathematical Modeling of COVID-19 with Periodic Transmission: The Case of South Africa

Abstract

The data on SARS-CoV-2 (COVID-19) in South Africa show seasonal transmission patterns to date, with the peaks having occurred in winter and summer since the outbreaks 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 analyzed. We note that if R₀ < 1, the disease-free equilibrium is globally asymptotically stable, and the disease completely dies out; and when R₀ > 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 indicate the need to consider seasonality in the transmission dynamics of COVID-19 and its importance in modeling fluctuations in the data for new cases. The potential impact of seasonality in the transmission patterns of COVID-19 and the public health implications is discussed.