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

Campillo-Funollet, Eduard and Wragg, Hayley and Yperen, James Van and Duong, Duc-Lam and Madzvamuse, Anotida (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). ISSN 1364-503X

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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’.

Item Type:
Journal Article
Journal or Publication Title:
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600
Subjects:
ID Code:
184752
Deposited By:
Deposited On:
24 Jan 2023 09:25
Refereed?:
Yes
Published?:
Published
Last Modified:
24 Jan 2023 09:25