In this thesis, we present a study to obtain a clear and accurate overview of the progress and behaviour of COVID-19 in the Netherlands. We distinguish two parts for this study. The first part is to estimate the total number of infected people as a function of time by combining data from hospital admissions, daily reported cases and serological data. Using these data sets, we found that our estimation for the number of infected people was comparable to the estimations provided by the RIVM and Sanquin. Furthermore, we found that on average only 39.3% of the total number of cases were detected. 1.2% of the total number of infected people is admitted to the hospital and 18.6% of the hospitalized patients is admitted to the ICU. The second part is to develop a representative model that reproduces the estimated total number of infections using a modified SEIR model. These modifications include modelling the infection rate β(t) as a function of time using a simple linear ODE, a system of ODEs inspired by the Lotka-Volterra equations, the implementation of gamma distributed exposed and infected stages and lastly the incorporation of spatial heterogeneity. We found that our Lotka-Volterra inspired model was able to model multiple consecutive waves, which differs from the standard compartmental models. The other modifications however seemed to have only minor effects on the model and had some difficulties with matching historical data. We conclude that our Lotka-Volterra inspired model should be used to model consecutive waves for a longer period of time. The other modifications can be used to optimize the model.

Experimental data have been extracted from wound-healing time-lapse videos. These data include the detection of the area of the wound and the detection of individual cells. Extracting the area of the wound is done by using a function in Python OpenCV called cv2.findcontours. An improved method to extract the area of the wound is introduced as well using the Sobel filter. Detecting the individual cells is done by localizing the local maxima in an image. Histogram equalization is applied to enhance the global contrast to increase the performance of cell detection. The continuum model is applied in one of the videos, where we used different parameters to model the data. A method is described to nd the optimal parameter of the continuum model by using the method of least-squares. Finally, two methods using the kernel density estimation are described which can be useful in future studies.