In this paper, we investigate the forced waves of a delayed diffusive endemic model with a shifting transmission rate. Here a forced wave is a traveling wave with wave speed the same as the environmental shifting speed. By constructing a new pair of upper-lower solutions, we prove the existence of forced waves for any negative shifting speed which corresponds the deceased of the disease, regardless of the magnitude of the delay. Moreover, we also derive the existence of forced waves with small shifting speeds without delay which signify the disease spread. A non-existence of forced wave when the limiting reproduction number is less than one is also proven.
關聯:
Journal of Mathematical Analysis and Applications 540(2), 128647
