Abstract
In this study, we developed a mathematical framework, based on the SIR model, to study the dynamics of two competing virus variants with different characteristics of transmissibility, immune escape, and cross-immunity. The model includes variant-specific transmission and recovery rates and enables flexible parameterization of partial and waning cross-immunity. We conducted stability and bifurcation analyses and numerical simulations to explore the conditions of coexistence, dominance, and extinction of the variants, studying variations in epidemiological parameters that affect endemic prevalence and infection ratios. Our results indicated that transmission rates, levels of cross-immunity, and immunity waning rates are critical in determining disease outcomes, which influence variant prevalence and competitive dynamics. The sensitivity analysis provided the relative importance of these parameters and provided valuable insight into designing intervention strategies. This work contributes to furthering our understanding of multi-variant epidemic dynamics and lays the bedrock for tackling complex interactions involving arising virus variants, finding applications in real-world public health planning.