Epidemic spreading model

This Master Thesis proposes a new mathematical method for modelling infectious diseases that spread in spatially separated populations at the same time, this is, pandemics. Pandemics have been simulated successfully by metapopulation models, which understand these separated populations as nodes of a network that are related among them by mobility patterns and where the transmission occurs within each one of the nodes independently. Even though we can find multiple modifications to this basic proposal in the literature, one assumption is always met: the mixing of the population during the spreading step is homogeneous, this is, there is the same probability of contact to every individual at the node. However, this is not realistic, as it is known that depending on the demographic group and area of residence of the individual, it is more probable to have a certain amount of contacts than another (i.e., kids tend to have more close contacts that any other age group because of going to school). Our proposal to produce more accurate results with this kind of model has been to incorporate to a basic metapopulation model an heterogeneous mixing within each subpopulation by means of networks that relate individuals. With the aim of testing whether scalar metrics employed in homogeneous schemes such as the average number of contacts are enough to define the ratio of infected individuals for different probabilities of infection, we tested our model over three different degree distributions --Poisson, power law and based on age demographics-- under the same circumstances and them compared them to an equivalent homogeneous approach. Results showed that the distribution of social contacts is a variable of relevance to define the spreading of an infectious disease