Existence of a nontrivial periodic solution in an age-structured SIR epidemic model with time periodic coefficients

In this paper, we are concerned with an age-structured SIR epidemic model with time periodic coefficients. We obtain the basic reproduction number ℛ0ℛ0 as the spectral radius of the next generation operator and show that it plays the role of a threshold value for the existence of a nontrivial periodic solution, that is, the model has a nontrivial periodic solution if ℛ0>1ℛ0>1, while no nontrivial periodic solution if ℛ0<1ℛ0<1. For the proof, we use a fixed point theorem of Inaba (1990) [7] based on the Krasnoselskii fixed point theorem.