Abstract
Considering the importance of time delay phenomenon in disease transmission and the interdependence of time delay and spatial location, a reaction-diffusion SIR epidemic model with nonlocal time delay (or time-space time delay) is proposed and the travelling wave solutions are discussed. Specifically, we define the basic reproduction number and the critical wave speed . For every wave speed , the existence of travelling wave solutions is studied by using the upper–lower solutions, the fixed-point theorem and some limit techniques when . The nonexistence of travelling waves when for any or for any c>0 is also proved. Finally, the influence of time-delay on disease propagation, especially the critical wave speed, is discussed through analysis and simulations.
Disclosure statement
No potential conflict of interest was reported by the author(s).