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Inverse problem for a coupling model of reaction-diffusion and ordinary differential equations systems. Application to an epidemiological model

Author

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  • Verdière, Nathalie
  • Manceau, David
  • Zhu, Shousheng
  • Denis-Vidal, Lilianne

Abstract

This paper investigates an identifiability method for a class of systems of reaction diffusion equations in the L2 framework. This class is composed of a master system of ordinary differential equations coupled with a slave system of diffusion equations. It can model two populations, the second one being diffusive contrary to the first one. The identifiability method is based on an elimination procedure providing relations called input-output polynomials and linking the unknown parameters, the inputs and the outputs of the model. These polynomials can also be used to estimate the parameters as shown in this article. To our best knowledge, such an identifiability method and a parameter estimation procedure have not yet been explored for such a system in the L2 framework. This work is applied on an epidemiological model describing the propagation of the chikungunya in a local population.

Suggested Citation

  • Verdière, Nathalie & Manceau, David & Zhu, Shousheng & Denis-Vidal, Lilianne, 2020. "Inverse problem for a coupling model of reaction-diffusion and ordinary differential equations systems. Application to an epidemiological model," Applied Mathematics and Computation, Elsevier, vol. 375(C).
    • Handle: RePEc:eee:apmaco:v:375:y:2020:i:c:s0096300320300369
    DOI: 10.1016/j.amc.2020.125067
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    References listed on IDEAS

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    1. Abid, Walid & Yafia, Radouane & Aziz-Alaoui, M.A. & Bouhafa, Habib & Abichou, Azgal, 2015. "Diffusion driven instability and Hopf bifurcation in spatial predator-prey model on a circular domain," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 292-313.
    2. Denis-Vidal, Lilianne & Joly-Blanchard, Ghislaine & Noiret, Céline, 2001. "Some effective approaches to check the identifiability of uncontrolled nonlinear systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 57(1), pages 35-44.
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    Cited by:

    1. Soradi-Zeid, Samaneh & Mesrizadeh, Mehdi, 2023. "On the convergence of finite integration method for system of ordinary differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).

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