Well Posedness and Control in a NonLocal SIR Model
Rinaldo M. Colombo, Mauro Garavello
Abstract
SIR models, also with age structure, can be used to describe the evolution of an infectious disease. A vaccination campaign influences this dynamics immunizing part of the susceptible individuals, essentially turning them into recovered individuals. We assume that vaccinations are dosed at prescribed times or ages which introduce discontinuities in the evolution of the S and R populations. It is then natural to seek the “best” vaccination strategies in terms of costs and/or effectiveness. This paper provides the basic well posedness and stability results on the SIR model with vaccination campaigns, thus ensuring the existence of optimal dosing strategies.
Topics & Concepts
VaccinationMathematicsClassification of discontinuitiesEpidemic modelOptimal controlStability (learning theory)Applied mathematicsMathematical optimizationMathematical economicsEconometricsDemographyComputer scienceMedicineMathematical analysisVirologyPopulationMachine learningSociologyMathematical and Theoretical Epidemiology and Ecology ModelsCOVID-19 epidemiological studiesMathematical Biology Tumor Growth