A big proportion of hospital-associated infections caused by Staphylococcus aureus can be attributed to Methicillin-resistant S. aureus (MRSA). Many countries take interventions to try and minimise the spread of MRSA. Interventions, such as a search-and-destroy policy and restrictive antibiotics use, have proven to be effective. Different strains of MRSA are grouped into clonal complexes (CCs) by their similarity to a central allelic profile. Separate MRSA CCs have evolved independently over time. In most countries a limited number of CCs is responsible for the prevalence in the population. In each country different CCs are present and the exact reasons why these CCs are successful in the specific countries is unknown. The aim of this project was therefore to study two different models, one implemented in R and one implemented in Java, that both simulate the spread of multiple MRSA CCs in a population. The two individual based models (IBMs) considered in this research produce similar results when setting them side-by-side using simple model set-ups. The R model turned out to be computationally expensive and very restrictive, where on the other hand, the Java model was much faster and more extensive. Consequently, the Java model was used to simulate the spread of MRSA CCs in a more advanced setting. Although the model set-up and population parameters were not yet realistic, it demonstrated some interesting findings. The general observation was that CCs with higher antibiotic resistance contribute most of the MRSA infections. The model showed that intervention by means of a search-and-destroy policy can lower the overall prevalence in a population significantly and create more variation between the CCs present. Since the model set-ups adopted during this research most likely do not completely agree with the biological processes, populations and interventions in the real world, future research should determine whether the obtained exploratory results also hold true in more representative populations.

Cholera is an infectious disease caused by the bacterium Vibrio cholerae. Infections can occur directly via contact with infected people, but also indirectly via infected water. Because of these direct, but especially indirect infections, it is useful to investigate the spread of the disease using mathematical epidemic models. In this report a compartmental epidemic model for cholera is discussed: the SIRB model. This model consists of four compartments: susceptibles, infected, recovered and the bacterial concentration in water. The interaction between the groups is given by a system of differential equations. The equilibrium solutions and their stabilityare mathematically analysed. The main focus of this report, however, is on two different spatial models. The patches model consists of multiple patches connected by migration of people. Different measures against cholera are studied using this model. The second spatial model that has been numerically implemented is a diffusion SIRB model. The influence of the diffusion coefficients on the solution patterns will be researched for different initial conditions. The results presented in this report are building blocks for further research into compartmental models that simulate the spatial dynamics of cholera.