Dynamical models in epidemiology and evolution

This thesis is concerned with the study of dynamical models in evolution for which some provide epidemiological insight. Two approaches are taken; one adopts the perspective of community dynamics, the other of adaptive dynamics. Community dynamics studies evolution via the dynamics of a fixed large number of strains, whilst adaptive dynamics begins by considering how one resident strain may be replaced by an advantageous mutant. The work begins by considering a baseline multi-strain host-pathogen model, and analysing it via a community dynamics approach. The baseline nature of the model allows exact information to be deduced. Obtaining such exact information is rare. Investigations into equilibrium co-existence states consisting of particular allowed numbers of host and pathogen strains are completed. The possibility of stable cycles occurring in these states is investigated. Analyses into the occurrence of contingencies (outcome dependent on initial conditions) between different states whether the equilibria are both point stable or point and sustained oscillations are completed. Investigations into invasion criteria for host and pathogen strains are presented.EThOS - Electronic Theses Online ServiceGBUnited Kingdo