Influenza poses a significant threat to global public health and socioeconomic stability. To account for the heterogeneity in vaccination coverage and contact patterns across different age groups, we develop a multi-group influenza model that incorporates population dynamics, incomplete immunity, and preferential mixing within each age group. Theoretically, the basic reproduction number \(\mathcal {R}_0\) is given by using the next-generation matrix approach, and through the persistence theory, the existence and globally asymptotic stability of both disease-free equilibrium and a unique endemic equilibrium is derived through the consistent persistence theory. Numerically, using the 2015-2016 influenza epidemic in Shenzhen as a case study, we estimate age-specific transmission rates, identifying preschool children as the most susceptible group, followed by school-aged students, the elderly, and adults. Sensitivity analysis reveals that preferential within-group contact raises \(\mathcal {R}_0\) due to clustering effects. The average contact level exhibits a nonlinear relationship with \(\mathcal {R}_0\) , which means there exists an optimal level that minimizes \(\mathcal {R}_0\) , while both excessive and insufficient contacts facilitate transmission. Vaccination, meanwhile, effectively reduces incidence. For example, the free-vaccination policy in Shenzhen significantly suppresses influenza transmission and reduces incidence among the elderly by 25.34% when targeting two key age groups. Gradient-based analysis further provides a quantitative basis for optimizing vaccination allocation across age groups. These integrated theoretical and numerical outcomes offer actionable insights for designing effective public health interventions.
