In my research I work on the mathematical theory of population dynamics and evolutionary genetics and apply it to real-world problems. Because evolution is a dynamical process, much of my research is concerned with dynamical systems theory, stochastic processes, optimization and computer simulations.
The primary focus of my work is to formalize and understand
(A) individual development (physiological, life-history)
(B) social interactions between individuals, and
the feedback between individual development, social interactions and ecological and evolutionary phenomena:
Multiscale dynamics in structured populations
A great challenge in understanding and predicting population and evolutionary dynamics is that individuals are different, they change during their lifetime. and that they are involved in many intertwined and complex processes. For instance, the recurrent spread of infectious diseases in an ecological community is affected by the age and spatial structure of the community, the interactions between hosts and other individuals in the community, and by the mutations in the pathogen and the host population altering e.g. the virulence of the pathogen or the immune system of its host.
A powerful method to model and analyze complex processes is to exploit the fact that some of them occur at vastly different timescales. Compare, for example, the rates at which pathogens and their hosts replicate. If processes operate on different timescales, the complex population model can be partitioned into smaller sub-models that can be analysed and assembled back together, gaining knowledge on the dynamics of the complex population. This is called multiscale analysis. It is a mechanistic method that enables population-level explanations and predictions to be made in terms of individual-level observables. For instance, it can be applied to understand how the spread of a disease is influenced by the feedback between within-host pathogen dynamics and the individual-level transmission of the pathogen in an age and spatially structured population. My interests and my recent work revolves around developing multiscale methods in structured populations by applying geometric singular perturbation theory, optimal control and dynamical systems theory. See my publications.
Applications in ecology, epidemiology and evolutionary biology
Supervised Master thesis
See my full publication list here