Spreading speed and traveling wave solutions of a reaction–diffusion Zika model with constant recruitment.

In this paper, we analyze spreading speed and traveling wave solutions of a reaction–diffusion Zika model with constant recruitment. By using the basic reproduction number R 0 of the corresponding ordinary differential system and the minimal wave speed c ∗ , the spreading properties of the solution of the model are established. More precisely, if R 0 < 1 , then the solution of the system converges to the disease-free equilibrium as t → ∞ and if R 0 > 1 , the entire solution of the system is uniformly persistent with ‖ x ‖ = c t , ∀ c ∈ [ 0 , c ∗) and the infectious disease gradually disappears with | x | ⩾ c t for any c > c ∗ . On the basis of it, we then analyze the full information about the existence and nonexistence of traveling wave solutions of the system involved with R 0 and c ∗. Finally, some numerical experiments are presented to modeling some conclusions. [ABSTRACT FROM AUTHOR]