Minimal wave speed and traveling wave in nonlocal dispersion SIS epidemic model with delay - Rassim Darazirar; Rasha M. Yaseen; Ahmed A. Mohsen; Aziz Khan; Thabet Abdeljawad (Boundary Value Problems)
Abstract This study examines traveling wave solutions of the SIS epidemic model with nonlocal dispersion and delay. The research shows that a key factor in determining whether traveling waves exist is the basic reproduction number R 0 $R_{0}$ . In particular, the system permits nontrivial traveling wave solutions for σ ≥ σ ∗ $σ ≥ σ ^{*}$ for R 0 > 1 $R_{0} > 1$ , whereas there are no such solutions for σ < σ ∗ $σ < σ ^{*}$ . This is because there is a minimal wave speed σ ∗ > 0 $σ ^{*}> 0$ . On the other hand, there are no traveling wave solutions when R 0 ≤ 1 $R_{0} ≤ 1$ . In conclusion, we provide several numerical simulations that illustrate the existence of TWS.