From data to mathematical analysis and simulation in models in epidemiology and ecology

This dissertation is divided into three different parts. In the first part we analyse collected data on the occurrence of influenza-like illness (ILI) symptoms regarding the 2009 influenza A/H1N1 virus pandemic in two primary schools of Trento, Italy. These data were used to calibrate a discrete-time SIR model, which was designed to estimate the probabilities of influenza transmission within the classes, grades and schools using Markov Chain Monte Carlo (MCMC) methods. We found that the virus was mainly transmitted within class, with lower levels of transmission between students in the same grade and even lower, though not significantly so, among different grades within the schools. We estimated median values of R0 from the epidemic curves in the two schools of 1.16 and 1.40; on the other hand, we estimated the average number of students infected by the first school case to be 0.85 and 1.09 in the two schools. This discrepancy suggests that household and community transmission played an important role in sustaining the school epidemics. The high probability of infection between students in the same class confirms that targeting within-class transmission is key to controlling the spread of influenza in school settings and, as a consequence, in the general population. In the second part, by starting from a basic host-parasitoid model, we study the dynamics of a 2 hosts-1 parasitoid model assuming, for the sake of simplicity, that larval stages have a fixed duration. If each host is subjected to density-dependent mortality in its larval stage, we obtain explicit conditions for coexistence of both hosts, as long as each 1 host-parasitoid system would tend to an equilibrium point. Otherwise, if mortality is density-independent, under the same conditions host coexistence is impossible. On the other hand, if at least one of the 1 host-parasitoid systems has an oscillatory dynamics (which happens under some parameter values), we found, through numerical bifurcation, that coexistence is favoured. It is also possible that ...