School of Mathematics

Jozsef Farkas

Jozsef Farkas abstract

Computing Science and Mathematics, University of Stirling

Structured models for disease dynamics

In this talk we are going to discuss partial differential equations, which we introduced recently to model infectious disease dynamics. Our models are extensions of basic SIS-type models, where the infected population is structured.  First we will introduce a model where structuring is with respect to pathogen load. Naturally, uninfected individuals correspond to the boundary state and we employ Wentzell-type boundary conditions to take this into account.  In the second model the infected population is structured with respect to the strain of the pathogen they are carrying. In general, individuals carrying different strains may have different infectiousness.  This assumption leads to a model with a highly nonlinear infection process replacing the classic mass-action assumption.  We prove global existence of solutions and establish existence of the endemic steady state for particular nonlinearities.