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

Abstract

COVID-19 is a disease caused by the novel coronavirus SARS-CoV-2 that emerged at the end of December 2019 and has since spread globally. In Kenya, the virus was first detected on 13 th March 2020. Soon after, the Kenyan government implemented non-pharmaceutical interventions (NPIs) to slow the spread of the disease. The pandemic continued to spread and it evolved into several waves over the years despite the discovery of vaccines and treatment. Mathematical models have been developed to help analyse, predict and simulate the dynamics of the pandemic. These models have largely been confined to single waves, without ready extension to multiple waves. In this paper, we develop a mathematical and computational model that can be extended to multiple waves using various concepts. Among these is the application of computational techniques that convert infection curves with negative gradients to those with positive gradients, in the neighbourhood of the change point, namely, where transition occurs from one wave to the next. This effectively generates a new wave. We then introduce a jump mechanism for the susceptible fraction, allowing further computation to align itself with the observed infection curve. To commence the process, we solved the system of governing ordinary differential equations for the period the epidemic spread without in- tervention and obtained values for the transmission, recovery and death rates that yielded the basic reproduction number, 0 2.76= , which is consistent with other related research. We then applied our model to COVID-19 in Kenya and the computation successfully replicated all the waves and also iden- tified the change points located within the months when COVID-19 variants became dominant. The findings strengthen the proposition that the dominant COVID-19 variants were the major drivers of the waves. The techniques can be extended to new strains of COVID-19, influenza and other respiratory viruses.