Forced Epidemic Waves in a Nonlocal Dispersal SIR Model with Shifting Transmission and Time Delay

Abstract

This paper is concerned with the forced epidemic waves of a nonlocal dispersal SIR model with shifting transmission and time delay. We first demonstrate that the existence of forced waves can be reduced to a fixed point problem. Then by constructing different pairs of upper and lower solutions and using Schauder's fixed point theorem, we establish two types of forced epidemic waves that reveal different state conversions of the disease. Moreover, we prove the nonexistence of forced epidemic waves when the basic reproduction number is less than unity. Finally, some biological explanations for the theoretical results are given in the discussion.