Nash-MFG equilibrium in a SIR model with time dependent newborn vaccination

Emma Hubert; Gabriel Turinici

doi:10.1007/s11587-018-0365-0

Nash-MFG equilibrium in a SIR model with time dependent newborn vaccination

Emma Hubert, Gabriel Turinici

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

We study the newborn, non compulsory, vaccination in a SIR model with vital dynamics. The evolution of each individual is modeled as a Markov chain. His/Her vaccination decision optimizes a criterion depending on the time-dependent aggregate (societal) vaccination rate and the future epidemic dynamics. We prove the existence of a Nash-Mean Field Games equilibrium among all individuals in the population. Then we propose a novel numerical approach to find the equilibrium and test it numerically.

Original language	English (US)
Pages (from-to)	227-246
Number of pages	20
Journal	Ricerche di Matematica
Volume	67
Issue number	1
DOIs	https://doi.org/10.1007/s11587-018-0365-0
State	Published - Jun 1 2018
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

Keywords

Individual vaccination
Mean Field Games
Nash equilibrium
SIR model
Vaccination
Vaccination efficacy
Vaccination games

Access to Document

10.1007/s11587-018-0365-0

Cite this

@article{c6fdeef896e64fb1bd4709c6a9adf9b1,

title = "Nash-MFG equilibrium in a SIR model with time dependent newborn vaccination",

abstract = "We study the newborn, non compulsory, vaccination in a SIR model with vital dynamics. The evolution of each individual is modeled as a Markov chain. His/Her vaccination decision optimizes a criterion depending on the time-dependent aggregate (societal) vaccination rate and the future epidemic dynamics. We prove the existence of a Nash-Mean Field Games equilibrium among all individuals in the population. Then we propose a novel numerical approach to find the equilibrium and test it numerically.",

keywords = "Individual vaccination, Mean Field Games, Nash equilibrium, SIR model, Vaccination, Vaccination efficacy, Vaccination games",

author = "Emma Hubert and Gabriel Turinici",

note = "Publisher Copyright: {\textcopyright} 2018, Universit{\`a} degli Studi di Napoli {"}Federico II{"}.",

year = "2018",

month = jun,

day = "1",

doi = "10.1007/s11587-018-0365-0",

language = "English (US)",

volume = "67",

pages = "227--246",

journal = "Ricerche di Matematica",

issn = "0035-5038",

publisher = "Springer-Verlag Italia s.r.l.",

number = "1",

}

TY - JOUR

T1 - Nash-MFG equilibrium in a SIR model with time dependent newborn vaccination

AU - Hubert, Emma

AU - Turinici, Gabriel

PY - 2018/6/1

Y1 - 2018/6/1

N2 - We study the newborn, non compulsory, vaccination in a SIR model with vital dynamics. The evolution of each individual is modeled as a Markov chain. His/Her vaccination decision optimizes a criterion depending on the time-dependent aggregate (societal) vaccination rate and the future epidemic dynamics. We prove the existence of a Nash-Mean Field Games equilibrium among all individuals in the population. Then we propose a novel numerical approach to find the equilibrium and test it numerically.

AB - We study the newborn, non compulsory, vaccination in a SIR model with vital dynamics. The evolution of each individual is modeled as a Markov chain. His/Her vaccination decision optimizes a criterion depending on the time-dependent aggregate (societal) vaccination rate and the future epidemic dynamics. We prove the existence of a Nash-Mean Field Games equilibrium among all individuals in the population. Then we propose a novel numerical approach to find the equilibrium and test it numerically.

KW - Individual vaccination

KW - Mean Field Games

KW - Nash equilibrium

KW - SIR model

KW - Vaccination

KW - Vaccination efficacy

KW - Vaccination games

UR - http://www.scopus.com/inward/record.url?scp=85045135495&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85045135495&partnerID=8YFLogxK

U2 - 10.1007/s11587-018-0365-0

DO - 10.1007/s11587-018-0365-0

M3 - Article

AN - SCOPUS:85045135495

SN - 0035-5038

VL - 67

SP - 227

EP - 246

JO - Ricerche di Matematica

JF - Ricerche di Matematica

IS - 1

ER -

Nash-MFG equilibrium in a SIR model with time dependent newborn vaccination

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this