In this talk, we will discuss the stability of traveling wave fronts for nonlocal reaction diffusion equations with delay. We prove that, in the appropriate weighted $L_\infty$ spaces, the non-critical traveling wave fronts are globally exponentially stable, and the critical traveling wave fronts are globally algebraically stable. Moreover, we obtain the rates of convergence by weighted energy estimates. These results will be applied to a host-vector disease model, the generalized Nicholson blowflies model, and a modified vector disease model. These results generalize earlier works of Lv-Wang and Mei et al.

traveling wave fronts; stability; nonlocal nonlinearity