On the almost periodic and almost automorphic solution for linear renewal equations with infinite delay via reduction principle

We prove, for nonhomogeneous autonomous linear renewal equations with infinite delay, that if the forcing term is almost periodic (respectively, almost automorphic), then every bounded solution on the whole real line is also almost periodic (respectively, almost automorphic). Additionally, the existence of a bounded solution on the half -positive real line implies the existence of an almost periodic (respectively, almost automorphic) solution. Next, we present a result on uniqueness. To illustrate our results, we propose an application to an epidemic model with waning immunity.