**Financial support through the following projects:**

UID/MAT/00297/2019

UID/MAT/00297/2013

PEst-OE/MAT/UI0297/2014

PEst-OE/MAT/UI0297/2011

Monday, 8 June 2015, 3:30 p.m.

Lecturer: Nicolas Bacaër, IRD, Bondy, France

Title: "A stochastic epidemic model in a random environment"

Local: Room 1.6, Edifício VII

Faculdade de Ciências e Tecnologia, Quinta da Torre, Caparica

Abstract: In a random environment that is a two-state continuous-time Markov chain, the mean time to extinction of the stochastic SIS epidemic model grows in the supercritical case exponentially with respect to the population size if the two states are favorable, and like a power law if one state is favorable while the other is unfavorable.

Lecturer: Paulo Doutor, CMA-FCT-UNL

Title: "Voluntary and preventive vaccination in an epidemiological model with seasonality"

Abstract: For a SIR model with temporary immunity and time dependent transmission rate it is natural to also assume time dependent vaccination. The vaccination profiles depends on health policies and individual decisions based on collective and individual goals of disease control, and of the awareness of risk associated to both the disease and the illness. We define preventive vaccination strategies as those that for any sufficiently small number of infectious individuals the disease monotonically decays to zero and among them the optimal vaccination that minimizes the effort of vaccination. Also, we allow for voluntary vaccination, where individuals choose to be or not vaccinated upon the risk of vaccination versus the risk of the disease. This is a game theory formulation and we were able to define a Nash equilibrium vaccination strategy such that all individuals behave in a rational manner. We have shown the existence of both an optimal and Nash strategies in a general setting. In general, these strategies will not be functions but Radon measures.