Persistence of Traveling Fronts of the Musca Domestica Blowflies Model with Long-range Diffusion

We studied the traveling fronts of the Musca domestica blowflies model with long-range diffusion from geometric singular perturbation point of view. Using analogy between traveling waves and heteroclinic solutions of corresponding ODEs, we proved the persistence of these waves for sufficiently small dissipation. Namely, the population quantity will finally reach a steady state if it is nonzero at begin.