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In this paper, it is shown that the SIR epidemic model, with the force of infection subject to seasonal variation, and a proportion of either the prevalence or the incidence measured, is unidentifiable unless certain key system parameters are known, or measurable. This means that an uncountable number of different parameter vectors can, theoretically, give rise to the same idealised output data. Any subsequent parameter estimation from real data must be viewed with little confidence as a result. The approach adopted for the structural identifiability analysis utilises the existence of an infinitely differentiable transformation that connects the state trajectories corresponding to parameter vectors that give rise to identical output data. When this approach proves computationally intractable, it is possible to use the converse idea that the existence of a coordinate transformation between states for particular parameter vectors implies indistinguishability between these vectors from the corresponding model outputs.

Original publication

DOI

10.1016/j.mbs.2004.10.011

Type

Journal article

Journal

Mathematical biosciences

Publication Date

04/2005

Volume

194

Pages

175 - 197

Addresses

School of Engineering, University of Warwick, Coventry CV4 7AL, UK.

Keywords

Humans, Communicable Diseases, Epidemiologic Methods, Incidence, Prevalence, Seasons, Algorithms, Nonlinear Dynamics, Models, Theoretical