Dynamics of SIR model with vaccination and heterogeneous
behavioral response of individuals modeled by the Preisach
operator

J 2021

Dynamics of SIR model with vaccination and heterogeneous behavioral response of individuals modeled by the Preisach operator

KOPFOVÁ, Jana; Petra NÁBĚLKOVÁ; Dmitrii RACHINSKII and Samiha C. ROUF

Basic information

Original name

Dynamics of SIR model with vaccination and heterogeneous behavioral response of individuals modeled by the Preisach operator

Authors

KOPFOVÁ, Jana (703 Slovakia, belonging to the institution); Petra NÁBĚLKOVÁ (203 Czech Republic, belonging to the institution); Dmitrii RACHINSKII (372 Ireland, guarantor) and Samiha C. ROUF (840 United States of America)

Edition

Journal of Mathematical Biology, Heidelberg (Germany), SPRINGER HEIDELBERG, 2021, 0303-6812

Other information

Language

English

Type of outcome

Article in a journal

Field of Study

10101 Pure mathematics

Country of publisher

Germany

Confidentiality degree

is not subject to a state or trade secret

References:

Journal of Mathematical Biology

Impact factor

Impact factor: 2.164

RIV identification code

RIV/47813059:19610/21:A0000095

Organization unit

Mathematical Institute in Opava

DOI

https://doi.org/10.1007/s00285-021-01629-8

UT WoS

000669407800001

EID Scopus

2-s2.0-85104119078

Keywords in English

SIR model; Preisach hysteresis operator; Lyapunov function; Endemic equilibrium; Periodic orbit

Abstract

In the original language

We study global dynamics of an SIR model with vaccination, where we assume that individuals respond differently to dynamics of the epidemic. Their heterogeneous response is modeled by the Preisach hysteresis operator. We present a condition for the global stability of the infection-free equilibrium state. If this condition does not hold true, the model has a connected set of endemic equilibrium states characterized by different proportion of infected and immune individuals. In this case, we show that every trajectory converges either to an endemic equilibrium or to a periodic orbit. Under additional natural assumptions, the periodic attractor is excluded, and we guarantee the convergence of each trajectory to an endemic equilibrium state. The global stability analysis uses a family of Lyapunov functions corresponding to the family of branches of the hysteresis operator.

Cite

KOPFOVÁ, Jana; Petra NÁBĚLKOVÁ; Dmitrii RACHINSKII and Samiha C. ROUF. Dynamics of SIR model with vaccination and heterogeneous behavioral response of individuals modeled by the Preisach operator. Journal of Mathematical Biology. Heidelberg (Germany): SPRINGER HEIDELBERG, 2021, vol. 83, No 2, p. "11-1"-"11-34", 34 pp. ISSN 0303-6812. Available from: https://doi.org/10.1007/s00285-021-01629-8.

@article{54441,
   author = {Kopfová, Jana and Nábělková, Petra and Rachinskii, Dmitrii and Rouf, Samiha C.},
   article_location = {Heidelberg (Germany)},
   article_number = {2},
   doi = {https://doi.org/10.1007/s00285-021-01629-8},
   keywords = {SIR model; Preisach hysteresis operator; Lyapunov function; Endemic equilibrium; Periodic orbit},
   language = {eng},
   issn = {0303-6812},
   journal = {Journal of Mathematical Biology},
   title = {Dynamics of SIR model with vaccination and heterogeneous behavioral response of individuals modeled by the Preisach operator},
   url = {https://link.springer.com/article/10.1007%2Fs00285-021-01629-8},
   volume = {83},
   year = {2021}
}

TY  - JOUR
ID  - 54441
AU  - Kopfová, Jana - Nábělková, Petra - Rachinskii, Dmitrii - Rouf, Samiha C.
PY  - 2021
TI  - Dynamics of SIR model with vaccination and heterogeneous behavioral response of individuals modeled by the Preisach operator
JF  - Journal of Mathematical Biology
VL  - 83
IS  - 2
SP  - "11-1"-"11-34"
EP  - "11-1"-"11-34"
PB  - SPRINGER HEIDELBERG
SN  - 03036812
KW  - SIR model
KW  - Preisach hysteresis operator
KW  - Lyapunov function
KW  - Endemic equilibrium
KW  - Periodic orbit
UR  - https://link.springer.com/article/10.1007%2Fs00285-021-01629-8
N2  - We study global dynamics of an SIR model with vaccination, where we assume that individuals respond differently to dynamics of the epidemic. Their heterogeneous response is modeled by the Preisach hysteresis operator. We present a condition for the global stability of the infection-free equilibrium state. If this condition does not hold true, the model has a connected set of endemic equilibrium states characterized by different proportion of infected and immune individuals. In this case, we show that every trajectory converges either to an endemic equilibrium or to a periodic orbit. Under additional natural assumptions, the periodic attractor is excluded, and we guarantee the convergence of each trajectory to an endemic equilibrium state. The global stability analysis uses a family of Lyapunov functions corresponding to the family of branches of the hysteresis operator.
ER  -

KOPFOVÁ, Jana; Petra NÁBĚLKOVÁ; Dmitrii RACHINSKII and Samiha C. ROUF. Dynamics of SIR model with vaccination and heterogeneous behavioral response of individuals modeled by the Preisach operator. \textit{Journal of Mathematical Biology}. Heidelberg (Germany): SPRINGER HEIDELBERG, 2021, vol.~83, No~2, p.~''11-1''-''11-34'', 34 pp. ISSN~0303-6812. Available from: https://doi.org/10.1007/s00285-021-01629-8.

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