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 coexistence between the two hosts occurs even in the case without density-dependence. Analysis of this case has been based on methods of approximation of the dominant characteristic multipliers of the monodromy operator using a recent method introduced by Breda et al. Models of this type may be relevant for modelling control strategies for Drosophila suzukii, a recently introduced fruit fly that caused severe production losses, based on native parasitoids of indigenous fruit flies. In the third part, we present a starting point to analyse raw data collected by Stacconi et al. in the province of Trento, Italy. We present an extensions of the model presented in Part 2 where we have two hosts and two parasitoids. Since its analysis is complicated, we begin with a simpler one host-one parasitoid model to better understand the possible impact of parasitoids on a host population. We start by considering that the host population is at an equilibrium without parasitoids, which are then introduced as different percentages of initial adult hosts. We compare the times needed by parasitoids to halve host pupae and we found that the best percentage choice is 10%. Thus we decide to fix this percentage of parasitoid introduction and analyse what happens if parasitoids are introduced when the host population is not at equilibrium both by introducing always the same percentage or the same amount of parasitoids. In this case, even if the attack rate is at 1/10 of its maximum value, parasitoids would have a strong effect on host population, shifting it to an oscillatory regime. However we found that this effect would require more than 100 days but we also found that it can faster if parasitoids are introduced before the host population has reached the equilibrium without parasitoids. Thus there could be possible releases when host population is low. Last we investigate also what happens if in nature mortality rates of these species increase and we found that there is not such a big difference respect to the results obtained using laboratory data.