Return-to-normality in a piecewise deterministic Markov SIR+V model with pharmaceutical and non-pharmaceutical interventions (Q6139953)

This work presents an SIR-type epidemic model, formulated as a piecewise-deterministic Markov model, in which the epidemiology is modelled as a continuous-time deterministic process, while demographic turnover is modelled via a stochastic jump mechanism. The model allows for control by means of time varying non-pharmaceutical interventions and by vaccination. The aim is to control the epidemic in such a way that the number of infected individuals does not exceed a pre-determined value, with constraints on the intensity of control. The initial configurations (number of susceptible and infected individuals) for which it is possible to do this are characterized as a sub-level set of a function which is the solution of a Hamilton-Jacobi equation. Numerical examples are provided.