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Reformulating the susceptible–infectious–removed model in terms of the number of detected cases: well-posedness of the observational model

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Reformulating the susceptible–infectious–removed model in terms of the number of detected cases: well-posedness of the observational model. / Campillo-Funollet, Eduard; Wragg, Hayley; Yperen, James Van et al.
In: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 380, No. 2233, 20210306, 03.10.2022.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Campillo-Funollet, E, Wragg, H, Yperen, JV, Duong, D-L & Madzvamuse, A 2022, 'Reformulating the susceptible–infectious–removed model in terms of the number of detected cases: well-posedness of the observational model', Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 380, no. 2233, 20210306. https://doi.org/10.1098/rsta.2021.0306

APA

Campillo-Funollet, E., Wragg, H., Yperen, J. V., Duong, D.-L., & Madzvamuse, A. (2022). Reformulating the susceptible–infectious–removed model in terms of the number of detected cases: well-posedness of the observational model. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 380(2233), Article 20210306. https://doi.org/10.1098/rsta.2021.0306

Vancouver

Campillo-Funollet E, Wragg H, Yperen JV, Duong DL, Madzvamuse A. Reformulating the susceptible–infectious–removed model in terms of the number of detected cases: well-posedness of the observational model. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2022 Oct 3;380(2233):20210306. Epub 2022 Aug 15. doi: 10.1098/rsta.2021.0306

Author

Campillo-Funollet, Eduard ; Wragg, Hayley ; Yperen, James Van et al. / Reformulating the susceptible–infectious–removed model in terms of the number of detected cases : well-posedness of the observational model. In: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2022 ; Vol. 380, No. 2233.

Bibtex

@article{ae86e3f246594607850e10fa7a8870c1,
title = "Reformulating the susceptible–infectious–removed model in terms of the number of detected cases: well-posedness of the observational model",
abstract = "Compartmental models are popular in the mathematics of epidemiology for their simplicity and wide range of applications. Although they are typically solved as initial value problems for a system of ordinary differential equations, the observed data are typically akin to a boundary value-type problem: we observe some of the dependent variables at given times, but we do not know the initial conditions. In this paper, we reformulate the classical susceptible–infectious–recovered system in terms of the number of detected positive infected cases at different times to yield what we term the observational model. We then prove the existence and uniqueness of a solution to the boundary value problem associated with the observational model and present a numerical algorithm to approximate the solution.This article is part of the theme issue {\textquoteleft}Technical challenges of modelling real-life epidemics and examples of overcoming these{\textquoteright}.",
keywords = "existence, epidemiology, susceptible–infectious–recovered, observational model, uniqueness",
author = "Eduard Campillo-Funollet and Hayley Wragg and Yperen, {James Van} and Duc-Lam Duong and Anotida Madzvamuse",
year = "2022",
month = oct,
day = "3",
doi = "10.1098/rsta.2021.0306",
language = "English",
volume = "380",
journal = "Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences",
issn = "1364-503X",
publisher = "Royal Society of London",
number = "2233",

}

RIS

TY - JOUR

T1 - Reformulating the susceptible–infectious–removed model in terms of the number of detected cases

T2 - well-posedness of the observational model

AU - Campillo-Funollet, Eduard

AU - Wragg, Hayley

AU - Yperen, James Van

AU - Duong, Duc-Lam

AU - Madzvamuse, Anotida

PY - 2022/10/3

Y1 - 2022/10/3

N2 - Compartmental models are popular in the mathematics of epidemiology for their simplicity and wide range of applications. Although they are typically solved as initial value problems for a system of ordinary differential equations, the observed data are typically akin to a boundary value-type problem: we observe some of the dependent variables at given times, but we do not know the initial conditions. In this paper, we reformulate the classical susceptible–infectious–recovered system in terms of the number of detected positive infected cases at different times to yield what we term the observational model. We then prove the existence and uniqueness of a solution to the boundary value problem associated with the observational model and present a numerical algorithm to approximate the solution.This article is part of the theme issue ‘Technical challenges of modelling real-life epidemics and examples of overcoming these’.

AB - Compartmental models are popular in the mathematics of epidemiology for their simplicity and wide range of applications. Although they are typically solved as initial value problems for a system of ordinary differential equations, the observed data are typically akin to a boundary value-type problem: we observe some of the dependent variables at given times, but we do not know the initial conditions. In this paper, we reformulate the classical susceptible–infectious–recovered system in terms of the number of detected positive infected cases at different times to yield what we term the observational model. We then prove the existence and uniqueness of a solution to the boundary value problem associated with the observational model and present a numerical algorithm to approximate the solution.This article is part of the theme issue ‘Technical challenges of modelling real-life epidemics and examples of overcoming these’.

KW - existence

KW - epidemiology

KW - susceptible–infectious–recovered

KW - observational model

KW - uniqueness

U2 - 10.1098/rsta.2021.0306

DO - 10.1098/rsta.2021.0306

M3 - Journal article

VL - 380

JO - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

SN - 1364-503X

IS - 2233

M1 - 20210306

ER -