Modelli epidemiologici su reti bipartite

If epidemiological dynamics described by compartmental models are well studied on network structures and more generally on homogeneous mixing, few investigations have been conducted on the behavior of these models on bipartite graphs, where two families of nodes are present and edges may exist only between nodes belonging to different families. The dynamical behavior of these networks is relevant among other for all epidemiological processes that aim to model the transmission of pathogens between vectors and hosts. The biological source of inspiration for our work is the transmission of two etiological agents: one responsible for tick-borne encephalitis (TBE) and the other for the Lyme Borreliosis (LB). Both are important endemic diseases in northern hemisphere existing in discontinuous, woodland foci that harbor tick vectors and small mammalian hosts. These systems are particularly suited for a discrete dynamical system approach mainly for two reasons. First, tick's life cycle is divided in three stages and during each stage a tick takes a single blood meal on a different host. Second, the frequency distribution of ticks on hosts seems to follow a power law. Moreover the epidemiological cycle of TBE virus raises an intriguing question. In fact, it has been seen that the main route of transmission for TBE virus is the so-called cofeeding, i.e. the virus can be transmitted from an infected to a susceptible tick feeding on the same host without involving the host in the transmission process. This peculiar route of transmission introduces in the system a higher level of complexity respect to standard compartmental models. Therefore, our main interests are: -to develop models which describe the transmission process of LB pathogen and that takes in account the high complexity of the system; -to model the role of cofeeding in the transmission of TBE. Although the model we intend to develop and study is peculiar of veterinary epidemiology, our methodological goals are general. In fact, several epidemiological system can be modeled using bipartite graphs, in particular when coupled with a dynamical behavior that transmit the pathogen only between nodes that belong to one of the two families and that share a common neighbor of the other family. Consider, for example, influenza transmission during a flight or between students sharing the same classroom. If humans are represented as nodes of one family, and airplanes or classrooms as members of the other family, it is evident that the virus can only be transmitted among humans with the necessary condition that they are at the same time in the same airplane or classroom.