Dottorato in Matematica
28° ciclo
SEMINARIO DI DOTTORATO
Mercoledì 7 ottobre 2015 ore 10:10
(Aula Seminari di Matematica)
Valentina Clamer
MCMC METHODS APPLIED TO EPIDEMIC OUTBREAKS IN
SCHOOLS AND DYNAMICS OF HOST-PARASITOID
INTERACTION AND COEXISTENCE OF DIFFERENT HOSTS
In the first part of this thesis, we develop a discrete-time SIR model to
estimate the probabilities of transmission between children of the same
class, of the same grade but different class and of different grades. The
motivations for this analysis come from the attention that was given to the
A/H1N1 2009 flu pandemic that has made it possible to collect detailed data
on the epidemic spread in more typical contexts, especially schools that are
well known to represent hot spots for epidemic spread. Data on infection
during that pandemic were collected also among students of two primary
schools in Trento (Italy). Although the data obtained were not detailed, we
show how their analysis yields estimates of transmission rates within class,
grade or school, that appear consistent between the two schools and with
our general understanding. Since the data are only partially observable, the
by now classical approach of Markov Chain Monte Carlo Methods is followed
to make inference about the missing data and the unknown parameters.
In the second part, we present a model in which one parasitoid species
attacks two host species, extending the overlapping generation model
presented
by Murdoch et al. (1987). Conditions for coexistence can be explicitly found
when the interaction between each host and the parasitoid results in
equilibrium coexistence. We investigate, through numerical bifurcation,
whether parameter values leading to periodic solutions make coexistence
Dipartimento di Matematica
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easier. Beyond theoretical issues, a potential application of the problem
concerns the response of native Drosophila parasitoids to the recent invasion
of the orchard pest Drosophila suzukii as we can see from the data collected
by the Edmund Mach Foundation in San Michele (Italy).
Relatore:
Andrea Pugliese