On the existence and uniqueness of an inverse problem in epidemiology

Aníbal Coronel, Luis Friz, Ian Hess, María Zegarra

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


In this paper, we introduce the functional framework and the necessary conditions for the well-posedness of an inverse problem arising from the mathematical modeling of disease transmission. The direct problem is given by an initial boundary value problem for a reaction-diffusion system. The inverse problem consists in the determination of the disease and recovery transmission rates from observed measurement of the direct problem solution at the final time. The unknowns of the inverse problem are the coefficients of the reaction term. We formulate the inverse problem as an optimization problem for an appropriate cost functional. Then, the existence of solutions of the inverse problem is deduced by proving the existence of a minimizer for the cost functional. Moreover, we establish the uniqueness up an additive constant of the identification problem. The uniqueness is a consequence of the first order necessary optimality condition and a stability of the inverse problem unknowns with respect to the observations.

Original languageEnglish
Pages (from-to)513-526
Number of pages14
JournalApplicable Analysis
Issue number3
StatePublished - 2021
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2019 Informa UK Limited, trading as Taylor & Francis Group.


  • 49K20
  • 49N45
  • 92D25
  • 92D30
  • Inverse problem
  • SIS
  • X. U. Dinghua
  • control problem
  • identification problem


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