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 ℛ 0 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 ℛ 0 > 1 , while no nontrivial periodic solution if ℛ 0 < 1 . For the proof, we use a fixed point theorem of Inaba (1990) [7] based on the Krasnoselskii fixed point theorem.