Spreading dynamics of a diffusive epidemic model with free boundaries and two delays

Abstract A delayed reaction-diffusion system with free boundaries is investigated in this paper to understand how the bacteria spread spatially larger area from initial infected habitat. Under assumptions that nonlinearities are of monostable type and values satisfy some compatible condition, we show boundary problem well-posed discuss long-time behaviour solution (including spreading vanishing) terms spatial-temporal risk index. Furthermore, determine speed when occurs, first study distribution roots a transcendental equation containing polynomial degree four then establish existence uniqueness monotone delay-induced nonlocal semi-wave by employing approximation method, lower-upper solutions technique Schauder fixed point theorem. It shown time delays slow down bacteria.