Dynamic of a two-strain COVID-19 model with vaccination

Abstract

COVID-19 is a respiratory illness caused by an ribonucleic acid (RNA) virus prone to mutations. In December 2020, variants with different characteristics that could affect transmissibility emerged around the world. To address this new dynamic of the disease, we formulate and analyze a mathematical model of a two-strain COVID-19 transmission dynamics with strain 1 vaccination. The model is theoretically analyzed and sufficient conditions for the stability of its equilibria are derived. In addition to the disease-free and endemic equilibria, the model also has single-strain 1 and strain 2 endemic equilibria. Using the center manifold theory, it is shown that the model does not exhibit the phenomenon of backward bifurcation, and global stability of the model equilibria are proved using various approaches. Simulations to support the model theoretical results are provided. We calculate the basic reproductive number R1 and R2 for both strains independently. Results indicate that – both strains will persist when R1>1 and R2>1 – Stain 2 could establish itself as the dominant strain if R11, or when R2>R1>1. However, because of de novo herd immunity due to strain 1 vaccine efficacy and provided the initial stain 2 transmission threshold parameter R2 is controlled to remain below unity, strain 2 will not establish itself/persist in the community.

Keywords

• Two-strain COVID-19
• Vaccination
• Dynamical systems
• Reproduction number
• Bifurcation
• Lyapunov function