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

Eduard Campillo-Funollet; Hayley Wragg; James Van Yperen; Duc Lam Duong; Anotida Madzvamuse

doi:10.1098/rsta.2021.0306

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

Eduard Campillo-Funollet, Hayley Wragg, James Van Yperen, Duc Lam Duong, Anotida Madzvamuse^*

^*Corresponding author for this work

Bristol Medical School (PHS)

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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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 ‘Technical challenges of modelling real-life epidemics and examples of overcoming these’.

Original language	English
Article number	20210306
Number of pages	15
Journal	Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	380
Issue number	2233
DOIs	https://doi.org/10.1098/rsta.2021.0306
Publication status	Published - 15 Aug 2022

Bibliographical note

Funding Information:
H.W. was supported by the Higher Education Innovation Fund through the University of Sussex, J.V.Y. and D.-L.D. were supported by Brighton and Hove City Council, East and West Sussex County Council and the NHS Sussex Commissioners, and E.C.-.F. was supported by the Wellcome Trust grant no. 204833/Z/16/Z. This work was partly supported by the Global Challenges Research Fund through the Engineering and Physical Sciences Research Council grant no. EP/T00410X/1: UK-Africa Postgraduate Advanced Study Institute in Mathematical Sciences (A.M. and E.C.-F.). A.M.’s work was partially funded by grants from the Health Foundation (1902431) and the NIHR (NIHR133761) and by an individual grant from Dr Perry James (Jim) Browne Research Centre on Mathematics and its Applications (University of Sussex). A.M. is a Royal Society Wolfson Research Merit Award Holder funded generously by the Wolfson Foundation. Acknowledgements

Publisher Copyright:
© 2022 The Authors.

Keywords

epidemiology
existence
observational model
susceptible-infectious-recovered
uniqueness

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Campillo-Funollet, E., Wragg, H., Van Yperen, J., 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

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author = "Eduard Campillo-Funollet and Hayley Wragg and {Van Yperen}, James and Duong, {Duc Lam} and Anotida Madzvamuse",

note = "Funding Information: H.W. was supported by the Higher Education Innovation Fund through the University of Sussex, J.V.Y. and D.-L.D. were supported by Brighton and Hove City Council, East and West Sussex County Council and the NHS Sussex Commissioners, and E.C.-.F. was supported by the Wellcome Trust grant no. 204833/Z/16/Z. This work was partly supported by the Global Challenges Research Fund through the Engineering and Physical Sciences Research Council grant no. EP/T00410X/1: UK-Africa Postgraduate Advanced Study Institute in Mathematical Sciences (A.M. and E.C.-F.). A.M.{\textquoteright}s work was partially funded by grants from the Health Foundation (1902431) and the NIHR (NIHR133761) and by an individual grant from Dr Perry James (Jim) Browne Research Centre on Mathematics and its Applications (University of Sussex). A.M. is a Royal Society Wolfson Research Merit Award Holder funded generously by the Wolfson Foundation. Acknowledgements Publisher Copyright: {\textcopyright} 2022 The Authors.",

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Campillo-Funollet, E, Wragg, H, Van Yperen, J, Duong, DL & 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

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; Van Yperen, James et al.
In: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 380, No. 2233, 20210306, 15.08.2022.

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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

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Campillo-Funollet E, Wragg H, Van Yperen J, 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 Aug 15;380(2233):20210306. doi: 10.1098/rsta.2021.0306

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

Abstract

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Keywords

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