Most results in mathematical epidemiology are based on fairly strong assumptions of random mixing in susceptible populations. However, real contact networks display a high degree of complexity such that a more detailed description of the interactions is needed. Based on the framework graph theory, I'm trying to understand the effects of such heterogeneity on pathogen evolution in such complex host systems.
The interaction of species in ecosystems can be represented by networks, in which species either prey on each other (food webs or trophic networks) or where interactions between species are mutually beneficial (mutualistic networks). The criteria which determine the stability of such networks is different for trophic and mutualistic networks, however. Interactions between species in real eco-systems are both trophic and mutualistic and thus non-trivial situations can arise when mixing the two. Using simulations of species interactions on networks based on real data, I investigate the change in stability conditions for networks that are both mutualistic and trophic.
Phylodynamic inference estimates epidemiological parameters from pathogen sequence data that is collected during an epidemic outbreak. Until recently, the statistical models that have been employed made crude assumptions about the underlying dynamical model. I develop phylodynamic models that account for realistic epidemiological dynamics, such as SIR-type model.