Injectivity analysis using interval analysis: Application to structural identifiability

This paper presents a new numerical algorithm based on interval analysis able to prove that a differentiable function f:A⊂Rn→Rn is injective. This algorithm also performs a partition of the domain A in subsets Ai where, for all x∈Ai, the cardinality of f−1(f(x)) is constant. In the context of parameter estimation, we show how this algorithm provides an efficient and numerical method to study the structural identifiability of parametric models.