Minimal wave speed and traveling wave in nonlocal dispersion SIS epidemic model with delay

Abstract

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 ∗ $\sigma \geq \sigma ^{*}$ for R 0 > 1 $R_{0} > 1$ , whereas there are no such solutions for σ 0 $\sigma ^{*}> 0$ . On the other hand, there are no traveling wave solutions when R 0 ≤ 1 $R_{0} \leq 1$ . In conclusion, we provide several numerical simulations that illustrate the existence of TWS.

Keywords

• SIS model
• Minimal wave speed
• Traveling waves
• Basic reproduction number