Campillo-Funollet, Eduard, Wragg, Hayley, Van Yperen, James, 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). a20210306 1-15. 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:	Article
Keywords:	epidemiology, existence, observational model, susceptible–infectious–recovered, uniqueness, Algorithms, Epidemiological Models, Mathematics
Schools and Departments:	School of Life Sciences > Sussex Centre for Genome Damage and Stability School of Mathematical and Physical Sciences > Mathematics
SWORD Depositor:	Mx Elements Account
Depositing User:	Mx Elements Account
Date Deposited:	27 Sep 2022 15:24
Last Modified:	27 Sep 2022 15:30
URI:	http://sro.sussex.ac.uk/id/eprint/108185

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