Modeling the effects of cross immunity and control measures on competitive dynamics of SARS-CoV-2 variants in the USA, UK, and Brazil

Abstract

Mutation in the SARS-CoV-2 virus may lead to the evolution of new variants. The dynamics of these variants varied among countries. Identification of the governing factors responsible for distinctions in their dynamics is important for preparedness against future severe variants. This study investigates the impact of cross immunity and control measures on the competition dynamics of the Alpha, Gamma, Delta, and Omicron variants. The following questions are addressed using an n-strain deterministic model: (i) Why do a few variants fail to cause a wave even after winning the competition? (ii) In what scenarios a new variant cannot replace the previous one? The model is fitted and cross-validated with the data of COVID-19 and its variants for the USA, UK, and Brazil. The model analysis highlights implementations of the following measures against any deadlier future variant: (i) an effective population-wide cross-immunity from less lethal strains and (ii) strain-specific vaccines targeting the novel variant. The system exhibits a fascinating dynamical behavior known as an endemic bubble due to Hopf bifurcation. It is observed that the actual situation in which Omicron won the competition from Delta followed by no wave due to Delta may turn into a competitive periodic coexistence of two strains due to substantial disparity in fading rates of cross-immunity. Global sensitivity analysis is conducted to quantify uncertainties of model parameters. It is found that examining the impact of cross-immunity is as crucial as vaccination.