Seminario interdisciplinare
ore
14:30
presso VII piano
Migratory fluxes of humans and of insects of various species have favoured the spreading of
diseases world-wise. It is important
to stress that those epidemics can have strong social and economical impacts if not seriously controlled.
Only in 2010 in Brazil, one million infected individual of which 80,000 where hospitalised.
I shall present the SIR-Network model, introduced in Stolerman et al (2015), and revisite the SIR model with birth and
death terms and time-varying infectivity parameter β(t). In the particular case of a sinusoidal parameter,
we show that the average Basic Reproduction Number Ro, already introduced in Bacaer et al. (2006) is not
the only relevant parameter and we emphasise the role played by the initial phase, the amplitude and
the period. For a quite general slowly varying β(t) (not necessarily periodic) infectivity parameter all the
trajectories of the system are proven to be attracted into a tubular region around a suitable curve, which
is then an approximation of the underlying attractor. Numerical simulations are given and comparison
with real data from Dengue epidemics in Rio de Janeiro allow us to estimate the infectivity rate and make
predictions about what are the periods more at risk of infection.