Abstract
The problem of traveling wave solutions (TWS) for a nonlocal diffusive Zika transmission model with bilinear incidence was studied. More specifically, the system admits a nontrivial TWS if the threshold ℜ > 1 and c>c⁎, where c⁎ is the critical wave speed; the system admits no nontrivial TWS for ℜ > 1 and 0<c<c⁎ or ℜ ≤ 1. The proofs are based on sub- and super-solution methods, Schauder's fixed point theorem and Laplace transformation. We also explain the influence of model parameters on the transmission of Zika virus. Compared with the previous studies on nonlocal diffusive epidemic models, a major difficulty is the boundedness of TWS arising from the bilinear incidence. The main result helps us to provide some new perspectives for the TWS of the nonlocal diffusion epidemic model with multiple infectious compartments.
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