Spreading speed and traveling waves for a nonmonotone reaction–diffusion model with distributed delay and nonlocal effect

In this paper, spreading speed and traveling waves for reaction–diffusion model with distributed delay and nonlocal effect without monotonicity are investigated. It is shown that there exists the spreading speed c∗ which coincides with the minimal wave speed, and its limiting integral equation has an unique traveling wave with speed c > c∗, and no traveling wave with c < c∗. Moreover, the dependence of the spreading speed on the delay and the nonlocal effect is considered.