PhD Seminar - Sara Sottle MSc University of Trento

Title: "Time-varying epidemic transmission in heterogeneous networks"

Abstract:

We analyze some epidemic models by considering a time-varying transmission rate in complex heterogeneous networks. The transmission rate is assumed to change in time, due to a switching signal, and since the spreading of the disease also depends of connections between individuals, the population is modelled as a heterogeneous networks. We establish some stability results related to the behaviour of the time-weighted average Basic Reproduction Number (BRN). Later, a SEIR model which describes the measles disease is proposed and we show that its dynamics is determined by a threshold value, below which the disease dies out. Moreover, compared with models without the Exposed compartment, we could find weaker stability results. A control strategy with an imperfect vaccine is applied, to determine how it could effect the size of the peak. Due to the periodic behaviour of the switching rule, we are able to find a threshold for the spread of the disease. The results discussed are obtained in collaboration with Prof. Xinzhi Liu.