Title: Complicated epidemiological dynamics due to the waning and boosting of immunity 

Abstract: Immunity following natural infection or immunization may wane, increasing susceptibility to infection with time since infection or vaccination. Immunity can also be boosted upon re-exposure or re-vaccination. To capture the interaction of these epidemiological and immunological phenomena, we can formulate mathematical models in terms  of partial differential equations, integral equations, delay differential equations, or ordinary differential equations. In this talk, we explore the relationship between these formalisms, depending on the mechanism of boosting.

Combining analytical and some recently developed numerical tools, we uncover very rich dynamics of such systems, with a range of possible abrupt changes including Hopf, saddle-node, period doubling and torus bifurcations. In a few scenarios we find multistability of limit cycles, and show that this can explain some unusual observed post-pandemic patterns of respiratory infections.

Extending the models with age structure allows us to suggest vaccination strategies, which we illustrate with applications to pertussis and SARS-COV-2.

About the speaker: https://www.math.u-szeged.hu/~rost/

Video of the talk: https://www.youtube.com/watch?v=xUIOlCR9TPU