Work

Viability and control of a delayed SIR epidemic with an ICU state constraint

Year: 2024

Type: article

Abstract: This paper studies viability and control synthesis for a delayed SIR epidemic. The model integrates a constant delay representing an incubation/latency time. The control inputs model nonpharmaceutical interventions, while an intensive care unit (ICU) state-constraint is introduced to reflect the healthcare system’s capacity. The arising delayed control system is analyzed via functional viability tools, providing insights into fulfilling the ICU constraint through feedback control maps. In particular, we consider two scenarios: first, we consider the case of general continuous initial conditions. Then, as a further refinement of our analysis, we assume that the initial conditions satisfy a Lipschitz continuity property, consistent with the considered model. The study compares the (in general, sub-optimal) obtained control policies with the optimal ones for the delay-free case, emphasizing the impact of the delay parameter. The obtained results are supported and illustrated, in a concluding section, by numerical examples.

Source: ESAIM Control Optimisation and Calculus of Variations

DOI: 10.1051/cocv/2024083

Authors: Dimitri Breda, Matteo Della Rossa, Lorenzo Freddi

Institution: University of Udine

Language: English

Topic: Mathematical and Theoretical Epidemiology and Ecology Models

Subfield: Public Health, Environmental and Occupational Health

Field: Medicine

Domain: Health Sciences

SDG: Good health and well-being

Open Access status: hybrid

Estimated APC paid: