Stepanov oscillatory type solutions for renewal equations with infinite delay: Application to an epidemic model with waning immunity

We establish a new result on the reduction principle for nonhomogeneous autonomous linear renewal equations with the forcing term bounded by mean values.This result is then used, together with a variation of constants formula, to prove Stepanov's version of Massera and Bohr-Neugebauer-type results.We also investigate uniqueness conditions in both the linear and nonlinear cases.Finally, we apply our theoretical results to an epidemic model with waning immunity.