LAUSR

Abstract In this paper, we derive a two-group SIR epidemic model with latent period in a patchy environment by applying discrete Fourier transform. It is assumed that the infectious disease spreads between two groups and it has a fixed latent period. When the basic reproduction number R 0 > 1 , we prove that the system admits a nontrivial traveling wave solution for each admissible speed c (namely, c > c ⁎ , where c ⁎ is the minimal wave speed). We also show that there is no positive traveling wave solution ( ϕ 1 , ϕ 2 , φ 1 , φ 2 ) satisfying φ i ( ± ∞ ) = 0 , ϕ i ( − ∞ ) = S i 0 and ϕ i ( + ∞ ) = S ⁎ i when R 0 ≤ 1 and c > 0 , or R 0 > 1 and c ∈ ( 0 , c ⁎ ) , where i = 1 , 2 .