Propagation dynamics of a nonlocal time-space periodic reaction-diffusion model with delay

<p style='text-indent:20px;'>This paper is concerned with a nonlocal time-space periodic reaction diffusion model age structure. We first prove the existence and global attractivity of solution for model. Next, by family principal eigenvalues associated linear operators, we characterize asymptotic speed spread in monotone non-monotone cases. Furthermore, introduce notion transition semi-waves model, then constructing appropriate upper lower solutions, using results spread, show that case exist when their wave above critical speed, do not anymore less than speed. It turns out coincides case. In addition, obtained are actually waves Finally, numerical simulations various cases carried to support our theoretical results.</p>