A Mathematical Model for Multiple COVID-19 Waves Applied to Kenya

Abstract

The COVID-19 pandemic, which began in December 2019, prompted governments to implement non-pharmaceutical interventions (NPIs) to curb its spread. Despite these efforts and the discovery of vaccines and treatments, the disease continued to circulate globally, evolving into multiple waves, largely driven by emerging COVID-19 variants. Mathematical models have been very useful in understanding the dynamics of the pandemic. Mainly, their focus has been limited to individual waves without easy adaptability to multiple waves. In this study, we propose a compartmental model that can accommodate multiple waves, built on three fundamental concepts. Firstly, we consider the collective impact of all factors affecting COVID-19 and express their influence on the transmission rate through piecewise exponential-cum-constant functions of time. Secondly, we introduce techniques to model the fore sections of observed waves, that change infection curves with negative gradients to those with positive gradients, hence, generating new waves. Lastly, we implement a jump mechanism in the susceptible fraction, enabling further adjustments to align the model with observed infection curve. By applying this model to the Kenyan context, we successfully replicate all COVID-19 waves from March 2020 to January 2023. The identified change points align closely with the emergence of dominant COVID-19 variants, affirming their pivotal role in driving the waves. Furthermore, this adaptable approach can be extended to investigate any new COVID-19 variant or any other periodic infectious diseases, including influenza