Reformulating the susceptible-infectious-removed model in terms of the number of detected cases: well-posedness of the observational model.
- Resource Type
- Academic Journal
- Authors
- Campillo-Funollet E; Department of Statistical Methodology and Applications, School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, Kent CT2 7PE, UK.; Wragg H; Department of Engineering Mathematics, School of Computer Science, Electrical and Electronic Engineering and Engineering Maths, University of Bristol, Bristol BS8 1TW, UK.; Department of Mathematics, School of Mathematical and Physical Sciences, University of Sussex, Brighton, East Sussex BN1 9QH, UK.; Van Yperen J; Department of Mathematics, School of Mathematical and Physical Sciences, University of Sussex, Brighton, East Sussex BN1 9QH, UK.; Duong DL; Department of Mathematics, School of Mathematical and Physical Sciences, University of Sussex, Brighton, East Sussex BN1 9QH, UK.; School of Engineering Science, LUT University, Lappeenranta 53850, Finland.; Madzvamuse A; Department of Mathematics, School of Mathematical and Physical Sciences, University of Sussex, Brighton, East Sussex BN1 9QH, UK.; Department of Mathematics, University of Johannesburg, Johannesburg, South Africa.; University of British Columbia, Department of Mathematics, Vancouver, Canada.
- Source
- Publisher: The Royal Society Country of Publication: England NLM ID: 101133385 Publication Model: Print-Electronic Cited Medium: Internet ISSN: 1471-2962 (Electronic) Linking ISSN: 1364503X NLM ISO Abbreviation: Philos Trans A Math Phys Eng Sci Subsets: MEDLINE
- Subject
- Language
- English
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'.