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

**Place:** Seminar Room - Department of Physics - Via Sommarive 14 - Povo - Trento

at **14:00 p.m.**

**Valentina Clamer**-*PhD**in mathematics*

*Abstract:*

This final seminar will be divided into three different parts.

In the first part, we analyse collected data on 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 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. Moreover, the discrepancy found between median values of R0 and the average number of students infected by the first school case suggests that outside 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, I will present the dynamics of a 2 host-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, we found that coexistence is favoured and it is even possible in the case without density dependence. 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, I will present a host-parasitoid model to analyse raw data on D. suzukii and its parasitoids in the province of Trento, Italy, and to understand the possible impact of parasitoids on them. We found that, if parasitoids are introduced when the host population is at an equilibrium without them, the best percentage choice of parasitoids to halve host pupae in the shortest amount of time is 10%. Instead if we introduce them when hosts are not at equilibrium, 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 and this effect would be even stronger if mortality rates, as probably in nature, are higher. Thus there could be possible releases when host population is low.

**Supervisor: ** Andrea Pugliese