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Our results demonstrate that the dominance dynamics of cocirculating variants correspond to a selective sweep characterized by a system of multilogistic equations driven by population immunity. Moreover, we show that the detection time of newly introduced variants can be accelerated or delayed depending on their emergence conditions and the prevailing variant landscape. Finally, we demonstrate that the effectiveness of response strategies depends critically on the evolving genomic composition of the outbreak, highlighting trade-offs between surveillance sensitivity and intervention timing. We validate our framework by jointly fitting epidemiological and genomic data from the spread of the Ancestral, Alpha, Gamma, and Delta variants in the United States, Denmark, the United Kingdom, and Canada. 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