Traveling waves for a generalized SIRI epidemic model with distributed delays and nonlocal dispersion

This research examines the existence and nonexistence of traveling waves in a nonlocal dispersion SIRI epidemic model with distributed delays and a generalised nonlinear incidence function. Our findings indicate that the presence of traveling waves in the system is determined by the basic reproduction number R 0 . When R 0 exceeds a critical threshold of 1, there is a minimum wave speed u* > 0, in such a way whereas u > u*, the investigated system admits nontrivial traveling wave solutions. However, no nontrivial traveling waves solution exists in the case u < u*. Finally, numerical simulations are performed to show the presence of traveling waves in the system using some well-known nonlinear incidence functions that our study includes.