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This thesis presents several nonlinear mathematical models applied to ecoepidemiology and evolution. A detailed study involving predator-prey type models considering an alternative resource for the predator was carried out, investigating the situation of infection in the prey and in the predator on separate models. Such study served as a theoretical contribution to the investigation of problems such as bovine tuberculosis in wild animal species presented in a specific model. We also developed models to explain the evolution of alarm calls in species of birds and mammals. The theoretical framework adopted for those evolution models is that of Population Ecology. The models were developed using Ordinary Differential Equations (ODEs) to describe the population dynamics. The biological assumptions of the systems that we wanted to analyse were enumerated and explained.

Mathematical models for ecoepidemiological interactions, with applications to herd behaviour and bovine tuberculosis, and evolutionary interactions of alarm calls