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arXiv · 2110.00364

Reformulating the SIR model in terms of the number of COVID-19 detected cases: well-posedness of the observational model

Eduard Campillo-Funollet·Hayley Wragg·James Van Yperen·Duc-Lam Duong·Anotida Madzvamuse
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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 is typically akin of 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, we then prove the existence and uniqueness of a solution to the derived boundary value problem and then present a numerical algorithm to approximate the solution.

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Eduard Campillo-Funollet, Hayley Wragg, James Van Yperen, Duc-Lam Duong, Anotida Madzvamuse. 2021-10-01. Reformulating the SIR model in terms of the number of COVID-19 detected cases: well-posedness of the observational model. https://doi.org/10.1098/rsta.2021.0306

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