Seminar time: 10 am

Venue: Aula Di Fresco (Via del Castro Laurenziano 9, Rome - Faculty of Economics - 4th floor)

Speaker: Jasmina Djordjevic (Faculty of Sciences and Mathematics University of Niˇs, Serbia)

Title: Informations & filtering in stochastic modelling of epidemic disease

Abstract
Stochastic mathematical models are employed to understand environmental uncertainties and the behaviors of infectious agents, providing predictions of disease progression and informing public health interventions through stochastic optimal control methodologies. In our approach, we introduce uncertainty into the transmission rate, treating it as an observable signal that influences infected individuals. The transmission rate is modeled using various processes such as Itˆo diffusion, mean-reverting processes, L´evy jump processes, and time-changed Lévy processes. Classical SIR (Susceptible-Infected-Recovered) model is refined by introducing new groups of individuals based on observed disease spread dynamics. The well-posedness of all models is ensured, conditions for disease persistence or extinction are established, the existence of stationary distributions is demonstrated, sensitivity analyses are conducted, and stochastic optimal control strategies are derived to optimize prevention measures. Our goal is to utilize previous analyses and the information about infected individuals by constructing a filtration that characterizes the filter and conditional distribution for the transmission rate.