Entire solutions in a time-delayed and diffusive epidemic model

Abstract

This paper is concerned with entire solutions in the following time-delayed and diffusive epidemic model:∂∂tu1(x,t)=d1▵u1(x,t)-a11u1(x,t)+a12u2(x,t),∂∂tu2(x,t)=d2▵u2(x,t)-a22u2(x,t)+gu1x,t-τ,where di>0(i=1,2). 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∈R.