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This paper proposes a new fractal–fractional age-structure model for the omicron SARS-CoV-2 variant under the Caputo–Fabrizio fractional order derivative. Caputo–Fabrizio fractal–fractional order is particularly successful in modelling real-world phenomena due to its repeated memory effect and ability to capture the exponentially decreasing impact of disease transmission dynamics. We consider two age groups, the first of which has a population under 50 and the second of a population beyond 50. Our results show that at a population dynamics level, there is a high infection and recovery of omicron SARS-CoV-2 variant infection among the population under 50 (Group-1), while a high infection rate and low recovery of omicron SARS-CoV-2 variant infection among the population beyond 50 (Group-2) when the fractal–fractional order is varied.