A major factor in the spreading of viruses is human-to-human transmission, and human mobility is clearly linked to the spreading process of epidemics. If we hope to understand the evolution of an epidemic, then we must also understand the underlying mobility process and the interaction between the two.

We propose the Markov modulated process (MMP) model as a tool for modeling mobility processes. We take a link-based approach to the MMP model, where modulating actions are a joint combination of adding and removing a number of links. We demonstrate that for such an approach, the states of the Markov process must encode not only a modulating action, but also the current number of links in the graph. We further show that in this case, the number of states will increase with O(N⁶) where N is the number of nodes. We refer to this as the "unaggregated" MMP model, and we introduce the concept of state aggregation to create the "aggregated" MMP model which only requires O(N²) states.

We demonstrate that both the aggregated and unaggregated MMP models are able to match the average number of links in the simulated mobility process, capturing the long-term dynamics of the mobility process with high accuracy. Both the aggregated and unaggregated MMP models are also able to match the average number of links added and removed between two time steps, capturing the short-term dynamics with high accuracy. Finally, we demonstrate that for certain mobility processes, the aggregated MMP model is able to produce results which are indistinguishable from the unaggregated MMP model while requiring just O(N²) states compared to O(N⁶).

This thesis consists of two parts which are connected by the central theme of epidemics. In the first part, a website is designed for forecasting the number of cases of COVID-19 in the Netherlands. The forecasting is performed using the Network-Inference-Based Prediction Algorithm (NIPA). The first part of the thesis documents the design process and some of the challenges faced along the way. An explanation of the NIPA algorithm is presented, and its implementation on the website is discussed.

The second part of this thesis shifts the focus to the modeling of mobility processes. Human-to-human transmission is often the dominant viral transmission vector, and therefore the spreading of the virus is inextricably linked to human mobility. The Markov-modulated process (MMP) model has recently been proposed as a novel method for modeling mobility processes. Yang has developed a so-called "aggregated MMP model" which is able to capture several key dynamics of mobility processes with high accuracy. This research builds on Yang's results and proposes the "quantized MMP model" as an extension of Yang's aggregated MMP model. Compared to the aggregated MMP model, the quantized MMP model reduces the number of required states by a factor equal to the quantization step size q, improving the efficiency of the model.

The behavior of the quantized MMP model for different step sizes q is compared with the aggregated MMP model. The results show that the quantization error has zero mean, allowing the quantized MMP model to achieve similarly high model accuracy. The SIR dynamics of the quantized MMP model for different step sizes are tested extensively and the disease spreading performance is compared with the mobility process. The suitability of the MMP model for forecasting the evolution of epidemics is evaluated and discussed.