Dynamical analysis of the SVEIR-M epidemic model with age structure under media coverage

With the frequent emergence and spread of new infectious diseases, poses severe threats to public health, and the government often relies on non-pharmaceutical interventions to cope. Meanwhile, the impact of media information on public behavior and health awareness is increasingly significant, becoming an indispensable factor in epidemic prevention and control. This paper constructs an SVEIR-M infectious disease model integrating age structure and media coverage mechanisms, depicting the differences in individuals' acceptance of media information and the effectiveness of vaccination at different age stages. The model introduces complex factors such as immune waning, latent development age, and media information dissemination, and systematically analyzes the existence and stability of disease-free and endemic equilibrium points using partial differential equations and Volterra integral tools. It is proved that the basic reproduction number <i>R</i> ₀ plays a threshold role in characterizing the dynamical properties of the system, and the global stability of equilibrium points under different conditions is demonstrated by constructing Lyapunov functions. In addition, the uniform persistence of the system is analyzed, and the correctness of the theoretical analysis is verified through numerical simulations, discussing the impact of different intervention measures on epidemic development. The research results show that media publicity and vaccination can significantly reduce the infection and mortality rates, and their combination can more effectively control the spread of the epidemic.