Global behavior of a multi-group SIR epidemic model with age structure and an application to the Chlamydia epidemic in Japan

Abstract

In this paper, we are concerned with the global behavior of a multi-group SIR epidemic model with age structure. A similar model was studied in [T. Kuniya, J. Wang, and H. Inaba, Discrete Contin. Dyn. Syst. Ser. B, 21 (2016), pp. 3515-3550] under some restrictive assumptions. In this paper, we weaken some of these assumptions for the purpose of application, and show that the global behavior of our model is completely determined by the basic reproduction number R 0 : if R 0 < 1, then the disease-free equilibrium is globally attractive, whereas if R 0 > 1, then the endemic equilibrium is globally attractive. The proofs are done by constructing suitable Lyapunov functions for total trajectories in compact attractors. In the application, we consider the chlamydia epidemic in Japan in 2015, and compare the estimation results of R 0 in four special cases of our model: a homogeneous model, an age-independent two-sex model, an age-dependent one-sex model, and an age-dependent two-sex model. In conclusion, we see that R 0 for the chlamydia epidemic in Japan in 2015 is in the range 1.0148-1.0535, and the introduction of the age structure has more influence on the value of R 0 than that of the two-group structure.