Entire solutions in a time-delayed and diffusive epidemic model

This paper is concerned with entire solutions in the following time‐delayed and diffusive epidemic model: $\left\{\begin{array}{c}\frac{\partial }{\partial t}{u}_1(x\text{,}t)=d_1▵u_1(x\text{,}t)-a_{11}{u}_1(x\text{,}t)+a_{12}{u}_2(x\text{,}t)\text{,}\hfill \\ \frac{\partial }{\partial t}{u}_2(x\text{,}t)=d_2▵u_2(x\text{,}t)-a_{22}{u}_2(x\text{,}t)+g\left(u_1\left(x\text{,}t-\tau \right)\right)\text{,}\hfill \end{array}\right.$ where $d_i>0$ $(i=1\text{,}2)$ . Using comparison arguments, we establish the existence and its properties of entire solutions for the above system. Here an entire solution means a classical solution defined for all $t\in ‐{R}$ .