Modeling the Spread of Epidemics

Visualizing the Spread of COVID-19 and Applying a Markov-Modulated Process Model to Mobility Processes

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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.