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Title: Oscillatory behaviour on a non-autonomous hybrid SIR-Model
Author: Rocha, Eugénio
Keywords: SIR-models
Hybrid systems
Issue Date: 28-Apr-2019
Publisher: Springer
Abstract: We study the impact of some abstract agent intervention on the disease spread modelled by a SIR-model with linear growth infectivity. The intervention is meant to decrease the infectivity, which are activated by a threshold on the number of infected individuals. The coupled model is represented as a nonlinear non-autonomous hybrid system. Stability and reduction results are obtained using the notions of non-autonomous attractors, Bohl exponents, and dichotomy spectrum. Numerical examples are given where the number of infected individuals can oscillate around a equilibrium point or be a succession of bump functions, which are validated with a tool based on the notion of delta-complete decision procedures for solving satisfiability modulo theories problems over the real numbers and bounded delta-reachability. These findings seem to show that hybrid SIR-models are more flexible than standard models and generate a vast set of solution profiles. It also raises questions regarding the possibility of the agent intervention been somehow responsible for the shape and intensity of future outbreaks.
Peer review: yes
DOI: 10.1007/978-3-030-19432-1_3
ISBN: 978-3-030-19431-4
Appears in Collections:CIDMA - Capítulo de livro
FAAG - Capítulo de livro

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