Modeling and analysis of epidemic spreading in mobile agents

Every day humans have to face with different kinds of diseases; from the most common one, the flu, to others more dangerous for our lives, like the EBOLA virus or the AIDS that fill us with dread. The spread of the epidemic through a population can be explosive or can remain in a steady state over long time periods. The way the illness propagates not only depends on the disease parameters but also on the structure of the network of the populations. This thesis focuses on two different aspects of the epidemic spreading: the first one is to find a low-dimensional representation of a large epidemic dataset by using a dimensionality reduction algorithm, the second one is to find a numerical computation of the epidemic threshold by considering a mobile-agent based model. Regarding the first topic, the dimensionality reduction method considered was the isometric features mapping (ISOMAP), a nonlinear dimensionality reduction method that overcomes the limitations provided by other methods attempting to reduce the order of the representation and gives the possibility to recognize the macroscopic behaviour of the epidemics thanks to the low dimensional embedding provided. This low-dimensional description of epidemic spreading is expected to improve our understanding of the role of individual response on the outbreak dynamics, inform the selection of meaningful global observables, and, possibly, aid in the design of control and quarantine procedures. Hence, in other words, the questions that this thesis wants to answer about this problem are: "What ISOMAP is able to do for epidemic description?", "There exists a relationship among embedded points and the process parameters?", "What we can expect from the obtained representation?".Concerning the second issue, the main idea was to find a link between epidemic spreading (obtained by simulating a mobile-agent based model with time-varying interactions) and the time-varying network of interactions. Thus, the non-trivial problem is to understand if it is possible to estimate the epidemic threshold from the time-varying network properties. To this aim, the method used in this thesis is based on the percolation theory; this approach was already used in order to associate the epidemic threshold to the percolation threshold but considering an activity-driven network (often used to study epidemic spreading models) or a static network. In this work instead it is faced the case of mobile agents models.