Abstract:
Ecosystems are characterised by a wealth of highly complex interdependencies. Mathematical models have already contributed considerably to gaining a better understanding of prey-predator interactions and epidemic spread; however often, such models also lead to new problems: A classical example from prey-predator dynamics is the paradox of enrichment, which the second chapter of this thesis deals with. A very recent branch of research is the extension of epidemiological models by a pathogen population: Whereas infection transmission is usually modelled by direct contacts of infected and susceptibles, in the new approach the infection is spread by a pathogen population. In chapter 3 a new model is described where in addition to the pathogen population that moves freely in the environment the replication process in the host is integrated. In chapters 4 and 5, prey-predator models with prey infection are investigated. After the analysis of the local behaviour, all models are extended by diffusive spread of the species. Random changes of environmental conditions are integrated by perturbing the populations with density-dependent noise. All models presented in this thesis are related but not restricted to phytoplanktonzooplankton systems. In fact, the results lead to much more general conclusions about competition in ecosystems.