Dynamical complexity in age-structured models of the transmission of the measles virus: epidemiological implications at high levels of vaccine uptake.

Abstract

This article explores the effect of increasingly finely stratified age structure on the dynamical properties of deterministic metapopulation models of the transmission of the measles virus. The dynamical simplicity of earlier age-structured models is shown to break down once the age-specific force of infection is no longer assumed to be constant across all child age classes below 5 years of age. While the biennial epidemics characteristic of earlier models are still observed, additional higher period stable cycles arise and coexist with the biennial cycle. The existence of multiple stable limit cycles necessarily implies model sensitivity on initial conditions, and for certain parameter values, chaotic dynamics are observed. Using a novel parameterization of the magnitude of seasonal forcing we are also able to make more biologically relevant comparisons between the dynamics of age- and non-age-structured models than have hitherto been possible. The epidemiological significance of these results is discussed, and we demonstrate that perturbations of the kind produced by intensive vaccination programs can shift transmission dynamics between biennial and triennial cycles. The possible implications of this work for studies of intermittency and infection persistence are also considered.