Speaker : Felicia Maria G. Magpantay (University of Michigan)

Title: Mathematics of imperfect vaccines

Abstract:
The dynamics of vaccine-preventable diseases depend on the
underlying disease process and the nature of the vaccine.
In this talk I will present a general model of an imperfect
vaccine and the epidemiological consequences of different
modes of vaccine failure. In particular, these can have
contrasting effects on disease prevalence and transient
solutions, especially after the start of mass vaccination
programs. I will also present an application to pertussis,
a childhood disease that was once considered a candidate
for eradication. This highly infectious disease is still a
significant cause of child mortality in the world, and has
been reemerging in some countries that maintain high
vaccination coverage (e.g. USA, UK). Recent events have
highlighted how much we still do not know about the
mechanics of this disease and the type of immunity
rendered by infection and vaccination. I will discuss the
theoretical analysis that led us to a general stochastic
model of pertussis, and the ideas behind the
likelihood-based statistical inference methods (trajectory
matching and iterated filtering) used to estimate the
vaccine parameters.