Reformulating the SIR model in terms of the number of detected cases: well-posedness of the observational model and parameter identification

Compartmental models are popular in the mathematics of epidemiology for their simplicity and wide range of applications. Although they are typically solved as initial value problems for a system of ordinary differential equations, the observed data is typically akin of a boundary value type problem: we observe some of the dependent variables at given times, but we do not know the initial conditions. In this talk, I will present a reformulation of the classical SIR in terms of the number of detected positive infected cases at different times, and then the existence and uniqueness of a solution to the derived boundary value problem. Some results regarding parameter identification given infected data from Sussex region (UK) together with some numerical results will be presented at the end.

This is a joint work with E. Campillo-Funollet, H. Wragg, J. Van Yperen and A. Madzvamuse.

Preprint available here.

The event will be held only via https://unimeet.uni-graz.at/b/tan-b5q-noz-k0a