Understanding the seasonal/periodic reoccurrence of influenza will be
very helpful in designing successful vaccine programs and introducing
public health interventions. However, the reasons for seasonal/periodic
influenza epidemics are still not clear even though various explanations
have been proposed. In this talk, we present an age-structured type evolutionary epidemiological model of influenza A drift, in which the susceptible class is continually replenished because the pathogen changes genetically and immunologically from one epidemic to the next, causing previously immune hosts to become susceptible. Applying our recent established center manifold theory for semilinear equations with non-dense domain, we show that Hopf bifurcation occurs in the model. This
demonstrates that the age-structured type evolutionary epidemiological model of influenza A drift has an intrinsic tendency to oscillate due to the evolutionary and/or immunological changes of the influenza viruses.
(based on joint work with Pierre Magal).