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

Abstract

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 R0 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 R0<1, then the solution of the system converges to the disease-free equilibrium as t→∞ and if R0>1, the entire solution of the system is uniformly persistent with ‖x‖=ct,∀c∈[0,c∗) and the infectious disease gradually disappears with |x|⩾ct 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 R0 and c∗. Finally, some numerical experiments are presented to modeling some conclusions.