Multistability and finite-time extinction in opinion-coupled competing epidemics

This paper investigates a coupled competing-epidemics-opinion model incorporating finite-time extinction mechanism (FTEM). The proposed framework captures the nonlinear interactions between epidemic competition and adaptive opinion evolution, where public opinion dynamically regulates transmission behaviors and reshapes the long-term epidemic outcomes. Theoretical analysis and numerical simulations reveal that opinion dynamics significantly affect the equilibrium structure and stability of the system. When one epidemic possesses a stronger effective transmission capability, the competing epidemic may be driven to extinction within finite time, causing the system to converge to a single-epidemic equilibrium. In contrast, under certain parameter conditions, the system exhibits bistability and trajectories may approach a saddle-point coexistence equilibrium, showing strong dependence on initial conditions. Furthermore, the introduction of finite-time extinction indices fundamentally changes the nonlinear competitive responses of low-density epidemics. Smaller indices strengthen competitive suppression and accelerate epidemic elimination, whereas larger indices favor persistence. The results further demonstrate that opinion feedback can amplify or weaken epidemic competition by dynamically regulating transmission rates, leading to diverse evolutionary pathways and multistable behaviors.