<p>A series of epidemic models with asymptomatic infection and transmission heterogeneity are progressively developed and discussed in this paper. The aim is to explore the effect of asymptomatic infections and their management on disease dynamics. The effective reproductive numbers of three models are derived, and their global dynamical properties are proven by constructing appropriate Lyapunov functions. The sensitivity analysis of effective reproduction numbers is obtained by the PRCC method. The comparative result shows that the relevance of transmission, hospitalization and recovery rates of symptomatic patients weaken dramatically when asymptomatic infection is considered. Meanwhile, differences in the sensitivity of influences associated with asymptomatic infections further confirm transmission heterogeneity. It also reveals that vaccine coverage is a crucial factor that affects the dynamics of disease. Additionally, this study examines numerical simulations to assess the effectiveness of various sensitivity-related interventions. Both theoretical and numerical results consistently reveal that neglecting asymptomatic infection will underestimate the extent of infections. Moreover, considering the transmission heterogeneity of asymptomatic infection and strengthening the management for higher-transmission subgroup, can minimize critical vaccination coverage and achieve disease control.</p>