This thesis deals with the interplay between people and nature, especially with the mutual dependences and implications of people and rivers. Using a hypothetical city, which settles near a river due to economic advantages, a mathematical model is developed. This model is used to constitute the dynamics in this sociohydrological interplay. The following work consists of three parts. Firstly, we look at a model of Baldassarre et al. (2013), of which we provide an overview and reproduce the upcoming simulations. The model contains the damage due to flooding and the distance to the river. Additionally, it deals with the height of levees, which people can build, and the psychological aspect of flooding events, which is incorporated in the awareness of flood risk. Based on this work, the second part describes the development of an optimal control model with two control and three state variables. The distance to the river, the awareness of floods and the height of the levees are used as state variables. The control variables are the additional height of the levees and a parameter measuring the risk preference of people living in this community. We give different specifications of the functional forms and dynamics, and step by step we try to improve the model and make it more realistic. Finally, some preliminary steps to optimal control theory are taken. We look at a situation, where a social planner has to choose constant control variables over a finite time horizon. Additionally, we give an overview, on how this decision depends on initial conditions. Lastly, we consider relative differences of the objective function, if not the best constant control is chosen.