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Poster De Conférence Année : 2019

Defining and Testing Identifiability, Illustrated by a HIV model

Résumé

We question the notion of identifiability and its relation with the actual ability to achieve identification. We show that a boundedness hypothesis on the set of parameter is essential, that amounts in most practical situation to bounding the magnitude of parameters. In the formal definition of identifiability, one should be very careful with the parentheses and the order of quantifiers, mostly concerning the external controls. However, under some good hypotheses, this is unimportant since a single trajectory may stand for all trajectory. Without controls, a weaker property plays a similar role and is expressed by the non-vanishing of a Wrońskian determinant. Then, eliminating the state variables is enough to get an exhaustive summary and to test identifiability. This method is close to criteria encountered in Wu et al for HIV models that we will consider as an application. Differential algebra also gives rigorous upper bounds on the minimal number of measurement times to test local and global identifiability.
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Dates et versions

hal-02415749 , version 1 (17-12-2019)

Identifiants

  • HAL Id : hal-02415749 , version 1

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H V J Le Meur, François Ollivier. Defining and Testing Identifiability, Illustrated by a HIV model. 4th Workshop on Virus Dynamics, Oct 2019, Paris, France. 2019. ⟨hal-02415749⟩
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